The last one (without the answer) is based on compression algorithms. The sequence is just saying what you see in the previous element. describing how many of each recurring digit So: 1 is just a single One ie One one (11) 11 is Two Ones. (21) 21 is One 2 followed by One one (1211) 1211 is One one followed by One two followed by two Ones (111221) 111221 is Three ones, followed by Two twos, followed by One one( 312211) So the next in the sequence would be 13112221 Simple
I agree, the obvious answer is 25%. The given solution answers the question "Solve x/2 = 50%." Which *could* be read "What is 50% (when) divided by 2" but they ommit such clarifying words. Sure it isn't strictly necissary, but it's omition heavily implies another meaning. "Evaluate x = 50% / 2." The statement is deliberately subversive.
That 50% question is legitimately incorrect. This is why language literacy is just as important as mathematics literacy when participating in doing math.
Yeah. They answered “50% / (1/2)”. The question was what is “50% / 2”. They converted divided by 2 into 1/2, but forgot to change the division sign to a multiplication sign,
I guess if you REALLY want to you can still justify that the answer is 1. The question is "what is 50% divided by 2 ?" If you interpret it as "what is 50 per (cent divided by 2) ?" (which you have no reason to do, of course) you do get 1 as the answer.
The last pattern is the “look and say sequence”, starting at 1… The number after 312211 is 13112221, because there’s 1 3, 1 1, 2 2, 2 1… but they didn’t ask for the next number, they asked for the *last* number in the sequence… The last digits will alternate between 11 and 21, so this sequence never ends, so there is no “last number”… unless you take 312211 as the last number they gave you…
So the correct answer would be 1? Because they didn't read the sequences as big numbers, but rather a sequence of one digit numbers without spaces. And the last number (digit) of the last sequence (of 1 digit numbers) of the infinite whole sequence, is 1 because it always is 1 and it can't be anything else than 1.
But they not ask for the number (btw a Conway sequence), but "Can you figure out ...". So the answer must be "yes" when you can, otherwise "no" when you can't.
Is there a rule of the internet that "there's an XKCD for that?" Because I entirely agree with what I think is Tom's main complaint and the same as Randall Monroe voiced 18 years ago in XKCD 169: "communicating badly and then acting smug when you're misunderstood is not cleverness."
And for my less TL;DR commentary: #2: The order of operations "riddles" are so common online that this should be pretty easy. Note that it also highlights why BODMAS (or PEMDAS) doesn't even work: after M, you have 3+9-3+3; applying A next gives 12-6, which is 6. To get 12 you have to either use BODMSA or group as BO[DM][AS] or PE[MD][AS], applying addition and subtraction together. #3: I got "2, but they're going to tell me it's 3" because I think embedding maths notation implicitly groups that apart from the operations in the English text. At best, it's ambiguous (unlike #2, which is well-defined because it's all written in symbols). #5: The answer just straight-up lied about what the question was, so the video can *&^% right off with that one. #6: I see Tom missed the extra instruction "all you can use is addition" because it was spoken but not on the board. Which actually helps because the only thing you could use and then pretend is nothing is writing multiple 8s as one number. And then there's barely enough time to say "888 leaves 112, so plus 88 and plus however many are left as singles and I hope that works." #8: Tom's attempt imaginines extra '+' signs between the lines. I got to "do they want to ignore the first two lines and get 2 or join them into 1+1+1+1+11+1+1+1+11+1×0+1 = 30?" #9: The Look And Say Sequence is pretty instantly recognisable to sequence fans. Find it as OEIS A005150.
@@peterb5 The part about only using addition was the only way I got it quickly. You need 5 8's in the units column to make 0, carry 4. Then 2 more 8's in the tens column for 0, carry 2. Then 1 more 8 in the hundreds column for 0, carry 1.
@@peterb5 Oh damn... Yeah, really glossed over that one... I'm used to encountering variations of this question with a pretty standard stipulation that the four basic operators are allowed. I was mostly watching for the commentary anyway, though, since these types of questions are usually irritatingly trivial or just badly phrased.
#3 they clearly got wrong too. In mathematical writing it is completely standard that a formula surrounded by text is treated as a whole. You never have a part of the formula interact with the text, and then with the rest of the formula. So the answer is unequivocally 2.
My instinct was that the answer was 2, but realised it was too obvious, so re-read it to come up with the 'right' answer. But it just didn't 'seem' to look right, but I couldn't understand why. Sure, if you follow BODMAS, the answer is 3, but as I read the question, I couldn't see whatever seemed wrong with it. Your explanation makes it so clear, so thank you for putting me out of my misery!
As a PhD. from Oxford (or Cambridge) you should know that there is a convention about precedence of operations: multiplication precedes addition: a+b*c = a+(b*c) and not (a+b)*c, this is not left to what one "wants to do".
Oh, I at first thought he meant that (a+b)c=ac+bc. I mean (a+b)c is equivalent to doing addition first and then multiplication, and ac+bc is equivalent to doing multiplication first and then addition. On the other hand, this property has little to do with the example in the video, so you’re probably correct 😅
He should have known that but I also agree that when you are communicating maths you wouldn't write it in that way precisely because it confuses rather than illuminates what you are trying to convey.
for 1+1+1+1+1 question, there is no operation between the lines (no hanging +), so they are different independent statements and have no bearing on the last statement. The last question is a description of the digits in the previous number in the sequence. 1 is described as "a single one" aka "one one" aka 11. 11 is described as "two ones" aka 21, then "one two, one one" aka 1211, etc... Numberphile did a video on it.
I originally got 12, and then quickly changed my answer to 30 after I saw they had omitted the missing plus signs on the end of each line. I thought they maybe wanted you to concatenate them to make two 11s, but apparently not 😂
There are no symbols that join them in a vector. But in any case, it looks vertical, it would be a matrix with 3 rows and 1 column. my answer was 5 5 ...=2 No connection seen between each row.
The last question - key is to read the numbers aloud to get the next number - the first number is one one - 11 (which is second number) - so the third number is two ones or 21 - which is one two then one one etc
I have found the answer for the question left opened. And i have a Formula in getting what i got The answer is 13122111 And the cornerstone of the sequence is 21 And my formula i used to get my answer which proves the results of the previous group of series before the expectant is binomial triangle method but with a little bit of complexity in it.
The final one is just a matter of reading out and counting the numbers of the previous sequence. The first is one 1 (written as 11), next is 2 ones (written as 21), then one 2 and one 1 (1211), and so on. So the answer is 13112221. It's actually an interesting analogy to file compression algorithms :)
I really dislike these as a concept. Not the riddles themselves, but the whole "thing" around the riddles. The poorly written prompts, grammatical errors, taunting phrasing. Everything about these riddles feels like they're designed to prey on people who are easily influenced. They fish for engagement with every single aspect of their presentation.
For anyone curious, the trick to the last riddle is to express the previous term in words and interpret that worded expression literally as the next term in the sequence: 1 - first term 11 - "1" has one 1 (one 1 = 11) 21 - "11" has two 1's (two 1 = 21) 1211 - "21" has one 2 followed by one 1 (one 2, one 1 = 1211) 111221 - "1211" has one 1 followed by one 2 followed by two 1's (one 1, one 2, two 1 = 111221) 312211 - "111221" has three 1's followed by two 2's followed by one 1 (three 1, two 2, one 1 = 312211) So the next term would be 13112221 because "312211" has one 3 followed by one 1 followed by two 2's followed by two 1's (one 3, one 1, two 2, two 1 = 13112221)
I've seen #8 multiple times online, and there they say that since there is no + in between the 1 at the end and the beginning of a row, its 11. So you basically add 4 + 11 + 3 + 11 + 0 + 1 = 30. But yeah.
You can't just ignore the carriage return. How does that in any way make sense? It's clearly 3 unrelated lines, specifically 2 expressions, and 1 equation that you need to finish.
For problem #2 the same applies in programming. Programing languages have well-defined operator precedence rules which define the order of the operations, however adding parenthesis/brackets around the groups makes it easier to read/follow, especially for complex equations or logic checks.
18:16 Well, on that one, they aren't very clearly part of the equation. There are not math operators linking the first two lines to the last. The answer I got was a 5, another 5, and a 2.
You're missing the point. Due to the lack of rigor in all of the previous problems, you simply can't determine what the person who created the problem intends, because anything is acceptable if it leads to more people getting the answer wrong.
@@weirdlyspecific302 What the person intends is not relevant to my comment. Tom says the numbers are "very clearly part of the equation" and I'm saying that, because of the very lack of rigor you refer to, they are *not* _very clearly_ part of the equation.
The only thing that surprised me was the reaction to bodmas. Can you imagine doing algebra without bodmas? 5 + 3x would equal 8x if you just go from left to right. Having to write 8 + (3x) would be so stupid. And if algebra becomes tedious and difficult without it, every other part of maths would too because it is literally built on algebra.
There is actually a fairly interesting bit of mathematics related to the "look-and-say" sequence. John Conway showed that the ratio between adjacent terms approaches a constant, and gave a polynomial with integer coefficients, of which said constant is a root.
@@remischmitt9308 This is not true. The sequence grows (asymptotically) exponentially forever. The only starting number which results in a sequence that doesn't grow infinitely is 22, since that stays at 22.
@@remischmitt9308it's provably nonrepeating in the strict sense, i.e. it's nonperiodic. sure you'll see the same patterns reappear, but they will forever do so somewhat randomly.
50% divided by 2 can't be 1, since they never say that it's 50% of 1. So since it's not 50% of anything specific, but 50% in general, the answer is 25% of that thing that we don't know of. If we were to accept that it's 1/2, we get 1/2 divided by 2, which is 1/2*1/2 = 1/4 Also, it's not 1/2/2, but rather
They want you to assume that it is already half of 100% so it is already divided by 2. This question is written wrong for the type of answer they are looking for.
Wait are u guys seriously thinking number 5 is wrong 50% ÷ 2 50% = ½ ½ ÷ ² the number two's cancel each other so 1 is left But for using decimal i have no idea
When I first noticed these 'order of operation' type riddle short videos, they were almost always about fighting over notation; as if there somehow was ONE correct interpretation. Often the parties arguing genuinely did not know better, as they had their particular 'correct' notation drilled into them at school over and over again (and had eventually given up resisting). Now we have math professors join in and tell what we (the non-resigned) knew all along: The notation means what we agree the notation means, and if there is doubt we should really agree ahead of time. So, rejoice, math fans, we won! (thank you Tom).
The thing about any expression is that it is attempting to express something. So the correct answer to "3+3x3-3+3" and its friends is always "Express yourself more clearly!"
@@peterbrockway5990 I find that often there is some context present, like a particular computer language or a particular math model problem, that will make the expression fairly well-defined (I guess 'fairly well-defined' is an oxymoron). The 'fun' or 'riddle' part is to some extent that the context is removed. Would it help if I go, say, "(3 + (3x3) - 3) + 3"? I am happy to go along with "3+3x3-3+3" when I feel I know the context. Are you more stringent, to the point, where you would still go "express yourself more clearly" even if you think you might be able to guess from the context? To me the win in this video is that WHEN the context might not be clear, or maybe entirely missing, THEN the expression defaults to largely undefined (or "bad notation" in Tom's words).
I didn't see any comments on puzzle #8 but the first 2 lines are not part of the equation because they don't have a plus sign in the end. Completely legit, very subtle trick.
have you ever seen numbers written on multiple lines? Like long expansions of decimals of PI where you continue the digits on the next line because there isn't enough space on the first? 1 + 1 + 1 + 1 + 11 + 1 + 1 + 1 + 11 + 1 * 0 + 1 = 30, those pesky 11's clearly take up so much space on the blackboard they had to be split on multiple lines, much like PI.
#3 depends on how you read the problem. If you pause after "half of" then in constant speed say "2 + 2" then the answer is 2. But if you pause after "half of 2" then and "+ 2" then the answer is 3. The problem with word problems in math is that they are ambiguous and depends much on both context and how it is interpreted.
There is something so pleasing about seeing a maths professor get as frustrated with these videos as me! 😂 I also made the exact same mistake as you on #6…
20:05 13112221 basically saying how many numbers there is like 1 how many ones one like one 1(11) then how many ones(2)(21) so on didn't copy pls don't attack ke
Okay so question 3 doesn't make sense. By order of operations, you do parenthesis first, and switching notation (from linguistic to mathematical notation) it's grammatically implied to be separated ideas
20:24 It is the “look and say” sequence (it’s called something like that) and the next term is given by saying the number of a certain digit in order so the next one will be 13112221
I'm MSc math and do not always respond correctly to riddles, even though I've constructed some crazy (correct) proof's over the years. Now I feel better.
For problem #8 you have to ignore the two first rows because there are no functions between them. Even if you don't want to ignore them, you don't know if your supposed to add, subtract multiply or divide or what you're supposed to do, cant just assume that you're supposed to add it when it doesn't say so.
I'd say only the '50% question' is a legitimate logically wrong question, the rest are valid. Since it's riddles and not straightforward questions, the roman numerals question is definitely valid. And the one where they said the first 2 rows aren't the part of the equation is also correct since they didn't have any symbol at the end of the lines or at the start of them. About the last one, I'd say the answer is infinity since they said 'the last number in this sequence' and the sequence is divergent.
I already learned the trick to the last question but... Every time I see a question like this it reminds me that any finite series of numbers can represent the values of a carefully-chosen polynomial. Which values? Could be solutions for P(x)=0 or P(1),P(2),etc..
That last / bonus question likely doesn't have an end. You're basically saying how many digits of which digit as you read the number left to right. 1 One 1 -> 11 Two 1 -> 21 One 2, one 1 -> 1211 One 1, one 2, two 1 -> 111221 Three 1, two 2, one 1 -> 312211 Going on like this, I don't think there's a defineable end. However, if you were to go with the total number of a given digit in the order those digits appear, you do get a defineable result: 1 One 1 -> 11 Two 1 -> 21 One 2, one 1 -> 1211 Three 1, one 2 -> 3112 One 3, two 1, one 2 -> 132112 Three 1, one 3, two 2 -> 311322 Two 3, two 1, two 2 -> 232122 Four 2, one 3, one 1 -> 421311 One 4, one 2, three 1, one 3 -> 141231 Three 1, one 4, one 2, one 3 -> 31141213 Two 3, four 1, one 4, one 2 -> 23411412 Two 2, one 3, two 4, three 1 -> 22132431 32212314 23322114 32232114 23322114 which we've already done; we've hit a repeating loop.
"Can you figure out the last number in this sequence?" You got the rules wrong. The next on the sequence is 31112221. It is obvious it always ends in the number 1. So even if you go to infinity the last number is always 1.
@pulsar22 That's the first paragraph: I don't think there is a last value. I did figure out that you say how many of which digits (consecutively) there are followed by the digit in the order they appear. 1 11 21 1211 111221 312211 13112221 1113213211 31131211131221 13211311123113112211 11131221133112132113212221 3113112221232112111312211312113211 1321132132111213122112311311222113111221131221 See what I mean? It seems to keep going and going, never getting to a repeating point. If the question had asked what the *next* value was, I agree with you. It's an improperly asked question, like that "50% divided by 2" one.
Bodmas doesn’t apply to a sentence - it applies to mathematical notation. Once you describe the problem in words, the rules of verbal interpretation apply.
#8 you could argue 2 solutions Either consider that the first 2 lines are not part of the equation since there's no + sign at the end, which results in 2. Another way to look at this problem is the coding grammar where spaces within an equation are first trimmed and we get 1+1+1+1+11+1+1+1+1+11+1+1x0+1= 32
The 1+1+1… turned out to be 30… the lines wrapped around and there were two elevens in the middle of the list. One of the 1’s was multiplied by 0 so it disappeared. If I subtotaled, it would look like 4+11+3+11+1.
Riddles, when applied to certain disciplines, are frustrating. "Math riddles" are meant to trick you into applying that mindset to it. Question 8 uses it well. "The indented portion wasn't part of the equation." Where plenty of others have stated that's not normal mathematical practice.
For the 50% question, I think what they did is that since 50% is (50/100), they divided that by 2, i.e. 50/100/2 and the 50/100= 1/2 and since there was a 2 dividing (50/100) it would go in to the numerator making the eq look something like (1/2)×2, the two in numerator will cancel the 2 in denominator resulting in 1.
For #8, even if you consider the first two lines part of the equation, it's still not 12. There is no operation between the end of each line and the beginning of the next. So yes, they are trying to trick you, but also no, it is not clearly one equation.
I was able to do #6 in the allotted time, but only since I had some experience with these videos and know some of the patterns in their answers. I also had to use some weird tricks to find the answer quickly. First I asked, “how could adding 8’s give us a 0 in the one’s place?” The only reasonable answer is by adding 8 five times, which would give us 40. I could then use similar logic to set the other digits to 0. I thought “how many times do I need to add 8 to the tens place to turn the 4 in 40 into a 0?” Well, twice because 8 + 8 + 4 = 20, so 80 + 80 + 40 = 200. Lastly, the hundreds place needed one 8 added to the 2 from 200 to set the digit to 0. 8 + 2 = 10, so 800 + 200 = 1000. Then, to get rid of the zeros in our numbers, we replace them with other 8’s. So long as we add one 8 in the hundreds place, 2 in the tens, and one in the ones place, we’ll get 1000. That’s how we get 888 + 88 + 8 + 8 + 8 = 1000.
What I interpreted for 50% divided by 2 :- 50%/2 50% means 1/2 So substituting 50% by 1/2 We get, 1/2/2 Which can be written as 2/2 =1 I know this is wrong but this is what I got 😅
RE: order of operations The order we have exists because algebra is easier to do if you don't need brackets everywhere to make it clear 3X+5 means (3×X)+5 rather than the unintuitive 3×(X+5). Their teaching as a rule to kids who don't understand the reasoning is IMO part of the problem with the whole education there. No one writes such problems with numbers for anyone over 8 or 9 because by that time you're getting introduced to the basics of algebra and it stops being an issue.
Tom, with question 8, you failed to notice that there were no addition signs at the end of the first to lines to connect the three lines together as one equation. Hence, the video was correct with that question. I do, however, agree with you regarding question 5, he clearly said "divided by 2" not "divided by half".
#7 can be solved differently If you take 19 in base 10 and substract 1 you'll get 18 which 20 in base 9. I find this solution to be more rigourous and more mathematically correct
So here is my thought for #5.... if you divide any number by 2 then it means that what we will be getting is the half of that number.... For example if you divide 10 by 2 then its the half of 10 i.e 5. But i guess they rather divided it by 1/2 thinking that it would give half of 50% but they actually had to multiply it by 1/2. that's where they got it wrong... what do y'all think
Problem 2 is a matter of operator precedence rather than order. All operators with the same precedence can be evaluated in any order. In this context, infix operators are assumed. Polish and Reverse would be much better : bracket free.
The 1+1 and so on-equation is very clearly 2. There's no mistake, just confusion. On the new lines it doesn't start with '+'. That's a dead giveawey. The last one are just the look-and-say numbers.
I can accept that at the "puzzle" level Roman numerals are used and even a vague operation like "take" (removing a symbol) is an option. But, reciprocally and for consistency, I hope that all my answers that use these tricks will be accepted as valid. That is, I have the freedom to solve in other numerical bases, in other arithmetics (modular for example) in other languages, operate according to the meaning of the dictionary... and in general, jump freely between different rules that were not specified.
For #8, I was taught at school that if you have to change lines in an equation you need to say what are you doing next and follow it to the next line. Like in this case: 1+1+1+1+1+ +1+1+1+1+1+ 1+1x0+1 If it would be written like this then 12 is the correct answer. At least from what I was taught
That would double the plus signs. Now for plus signs this doesn't pose problems, but it would if you do this with minus signs. 4- -2 is actually 6, because it says 4 - -2. If you continue a line, just write the operator at the end of the first line: 1+1+1+1+1+ 1+1+1+1+1+ 1+1*0+1 or, preferably, at the start of the next line: 1+1+1+1+1 +1+1+1+1+1 +1+1*0+1 The last is prefered because here too, if the line were broken at a subtraction, then the minus sign would be close to the subtracted number.
For question 5 the answer is one because 50% is 50/100 if we divide that by 2 then we will get 50/100/2 which we can do 2 ways we can just divide and get 50/50 or we can multiply 2 with 50 and divide it by 100 = 100/100.
I agree, bad notation is bad! However most people who "understand" PEMDAS (or any variation of it) assume a logical order as follows. Left to right order because it's how we read (in English). A lot of people don't know that [M and D] and [A and S] have equal priority. Then, within that priority bracket we apply left to right logic. So for example 2(3 + 2)^3 = 250 because brackets/parentheses --> orders/exponents/powers --> multiplication. Alternative "solutions" may be 70 or 1000 but even with brackets here, it's not "obvious". My answer to the last question with way more than 15 seconds is: 131112121111 but it think that sequence is just - say what you see in the last sequence in words. Less than 1 min. Am I smart? Maybe? Dr. Tom Crawford is miles better than me at mathematics. I think the issue with people in extremely high academic standings is that they lose track of the basics when working on REALLY complex problems! I admire them greatly though!
I don't really like BODMAS or PEDMAS. I think it's wrong to imply that Division should be resolved before Multiplication and Addition before Subtraction. It may seem pedantic, but honestly I think it can cause confusion later in math. The students I've tutored seem to get this idea that Division and Multiplication (or Addition and Subtraction) are somehow fundamentally different from one another. Yes, they are technically different, but the difference is analogous to walking towards vs. away from something - you end up in different places, but in either case you are still walking (i.e. the action is the same). IMO it would be better to teach students that order of operations is about identifying parts of an equation (e.g. what are we trying to multiply? what are we taking the logarithm of? what are we adding together? etc.). Once you can identify the parts, order of operations becomes irrelevant. So long as you're consistent in the "what" of each operation, the math will always work out.
Yeah I guess if people rely only on the order of letters there and forget it's meant to be like PE(MD)(AS). I guess it could be simplified as PEFT for parenthesis exponents factors and terms? I may have an unpopular view on this but I'd go as far as to say there's no difference between addition and subtraction, and that it's a mistake to think of them as operands acting on two values. If you view the expression 3 - 4 as two terms, +3 and -4, suddenly the order doesn't matter despite it being subtraction (3 - 4 isn't 4 - 3) but the terms +3 and -4 evaluate to the same as -4 and +3, so 3 -4 = -4 + 3. I believe this way of thinking is commonly used already when simplifying expressions. Like 3 + 4 + 5 - 4 = (+4 and -4 cancels out) = 3 + 5, suddenly here we don't think of the - as an operand acting on 2 values. The exact same goes for factors, apart from rewriting 3 / 2 as /2 * 3 isn't exactly standard notation, but personally I think it makes sense. Edit: I say no difference, but obviously subtraction means the next term is negative. My point it wether it's addition or subtraction it's just a list of terms that have to be evaluated, positive or negative.
For the 1+1+1+1+1etc question, i assumed that the 5th and 6th, and 10th and 11th 1's were actually an 11 since there was no sign noted between them. Doing this I got an answer of 30. 1+1+1+1+11+1+1+1+11+1×0+1=30
For #6, there is another more likely to be a math solution. [(8 + 8) * 8 - (8 + 8 + 8) / 8] * 8 = 1000 8 + 8 = 16 16 * 8 = 128 (8 + 8 + 8)/8 = 3 * 8 / 8 = 3 128 - 3 = 125 125 * 8 = 1000 For #9, the "last number" is ambiguous. The sequence can continue forever, so you cannot say that a number is the last number, in mathematical sense.
Hey Tom! Idk if you’d be interested in this but the LSAT just removed their “logic games” section from the test, which tested lots of conditional logic. Would you consider doing an LSAT Logic Games section? Think it would be really cool to see! Keep up the good work on the vids
the one with all the ones is definitely 2 after looking back because at the end and beginning of each line there is no function so they can't be a apart of the same equation
Omg, i can't believe they don't have answer to #9. It's one of my favorites. It's 13112221. You almost had it when you said counting the ones. Each is count the amount of numbers in the previous. One, one one, two ones, one two and one one, One one and one two and two ones, Three ones and two twos and one one, Etc
What is 50% divided by 2. Think out of the box: There is another meaning to the sentence: (What, divided by 2, is 50%) => What becomes 50% when divided by 2. => ans: 1.
The first one is 50% / 2 = x And the second one is x / 2 = 50%. X1 = 25%, X2 = 100%. You can figure it out yourself tbh. "What, divided by 2, is 50%", is the same as ---> X, divided by 2, is 50% --> X / 2 = 50% X = 100%
My guess for #8 was 10. I knew _something_ was up without the plus signs, but from there, it was impossible to guess exactly what we were supposed to do. Since two numbers next to each other typically means multiply, I assumed the 1 from the previous row was supposed to be multiplied by the 1 from the next row, which going by PEMDAS, would equal 10. So yeah, there's no way to get that right without either getting lucky or being a mind reader, because even noticing the missing plus signs, I wasn't sure what the cartoon teacher wanted us to _do_ with that information.
But the log 2 requires a 2, which isn't allowed (only 8s!), * (multiplication) isn't allowed, and the 1024-24 is a subtraction, which also isn't allowed (only addition can be used, if you listen to the original question).
@@Mimik9X00 I admit the question didn't actually specify "only 8s", but if it had meant "eight 8s, together with ANY OTHER numbers you want to use", then there would be a huge number of solutions, which wouldn't make for a very interesting problem!
6:00 when i was a wee little lad in school they taught me PEMDAS or BEMDAS (their quite similar) parenthesis exponents multiplication division addition subtraction.
actually, 3+3×3 is quite clear because it didn’t have brackets. It’s obviously the multiplication that should be perform first it is just you who confused the order between multiplication and addition
Is it half of 2... plus 2 (three). But I clearly heard "What is half... of 2+2" (two). These kind of interpretive questions are REALLY maddening because both answers can be correct depending on how you ask the question.
#7 first two lines are not part of the equation because there are no connecting operator between line 1 to line 2 and from line 2 to line 3. If you are a sharp computer programmer you would notice this immediately because what is written on the board would give a syntax error.
7th riddle is actually very easy ,because they're asking a yes or no question, and based on the previous riddles what they mean is how do you do it, but that is not what they wrote. and by that logic you can with good confidence just answer yes without even knowing if its right or not.
The voice over did say you could only use addition even though that was not written on the screen, so whilst your answer is valid if other operations other than addition were permitted, it is not when addition only is permitted. Also to present you answer you had to use the digits 1, 2 and 3. The question clearly said to use only 8's.
I think that the 'problem' with a well qualified mathematician attempting to solve these puzzles is that 'proper' mathematicians look too deeply in to them for an answer. I'm an accountant, so good at 'simple' maths, but I wouldn't call myself a 'mathematician'. For the '1000 using eight 8s' puzzle, the instruction that 'addition' was the only operation allowed, i quickly deduced that you need to add five numbers that end with '8' in order for the last digit to be zero. So now I have three 8s left. 88 + 88 + 88 plus two eights will be nowhere need 1000, so one number must be '888'. Then I've only got one more '8' to 'play with', so there must be an '88'. A quick check shows this must be pretty close and is the only solution that is, so must be the right one. So it is possible in 15 seconds. Each number in the last question describes the order of digits in the previous number, so the '11' given as the second number isn't 'eleven', but says 'One 1' (because the previous number contains one 1, but no other digits). The fourth number (1211) effectively says 'One 2, One 1' (explaining the '21' given just before). So the first missing answer is 'One 3, One 1, Two 2s, Two 1s' (13112221). I didn't get the Roman Numeral question right, but would agree that although 'BODMAS' or 'PEDMAS' is taught in school, puzzles involving orders of operations could often be notated better.
the last one is actually a clever sequence i'd gotten acquainted with decades ago. i call it the "whatchu got?" sequence ...or the "read it back to me" sequence. it goes like this: start with 1: 1 "ok, whatchu got?" "i got one 1." 11 "whatchu got now?" "two 1s." 21 "now whatchu got?" "one 2, one 1." 1211 [...] "one 1, one 2, two 1s." 111221 312211 13112221 1113213211 . . . it has i don't know its oeis#, but it has a fancy name. last i checked it had no explicit formula, but many papers have been written about it, several standing/unresolved/unproven conjectures. it resembles a fractal... a 1-d aperiodic tiling...
I actually got #6, but wasn’t 100% certain I was right in the time. They said using only addition, so I figured concatenation had to be legal. We were never going to get anywhere near it if we didn’t do 888. This leaves us a bit over 100 away, and they told us it was 8 8s, so I figured it was 888 + 88 + 8 + 8 + 8, because 888 + 88 + 88 + 8 would over shoot, but I was still working out if it was exactly 1000 when time ended.
Watch the original video from Bright Side here: ua-cam.com/video/r5P-f5arPXE/v-deo.html
Your video is very nicely done
Better than theirs lol
The last one (without the answer) is based on compression algorithms. The sequence is just saying what you see in the previous element. describing how many of each recurring digit So:
1 is just a single One ie One one (11)
11 is Two Ones. (21)
21 is One 2 followed by One one (1211)
1211 is One one followed by One two followed by two Ones (111221)
111221 is Three ones, followed by Two twos, followed by One one( 312211)
So the next in the sequence would be
13112221
Simple
u need pre-school 4 cheating :)
@@KenFullman ha nice
try solving IOQM exam from India
Waiiiiiiit whattt?! #5 says 50% divided by 2, not 50% divided by 1/2, they’re so gaslighting us!
This is not just annoying, its crazy! They _are_ wrong!
its 1/4 or 25%
50% is 1/2 and deviding it by 2 means 1/2 * 1/2
95% of people don't understand percentages, so they easily get away with it.
Almost fooled Tom as well ;-)
I agree, the obvious answer is 25%.
The given solution answers the question
"Solve x/2 = 50%."
Which *could* be read
"What is 50% (when) divided by 2"
but they ommit such clarifying words.
Sure it isn't strictly necissary, but it's omition heavily implies another meaning.
"Evaluate x = 50% / 2."
The statement is deliberately subversive.
Xd how you messed up Question 2? 😅 @@mlloser8318
A great example of "writing my 'riddles' ambiguously to make the reader feel like a donkey".
😂😂
That 50% question is legitimately incorrect. This is why language literacy is just as important as mathematics literacy when participating in doing math.
it was probably also incorrect on purpose to drive engagement in the comments
@@MegaOoga That is the problem. This gives birth to Terrance Howard's of the future
Yeah. They answered “50% / (1/2)”. The question was what is “50% / 2”. They converted divided by 2 into 1/2, but forgot to change the division sign to a multiplication sign,
I guess if you REALLY want to you can still justify that the answer is 1.
The question is "what is 50% divided by 2 ?"
If you interpret it as "what is 50 per (cent divided by 2) ?" (which you have no reason to do, of course) you do get 1 as the answer.
The last pattern is the “look and say sequence”, starting at 1…
The number after 312211 is 13112221, because there’s 1 3, 1 1, 2 2, 2 1… but they didn’t ask for the next number, they asked for the *last* number in the sequence…
The last digits will alternate between 11 and 21, so this sequence never ends, so there is no “last number”… unless you take 312211 as the last number they gave you…
Yes, I also recognized the John Conway sequence from the Numberphile video.
@@thomashoglund5671 The Conway sequence is the look-and-say sequence starting with a 3, specifically, instead of a 1.
Thank you "please don't touch anything" for introducing me to this sequence
So the correct answer would be 1? Because they didn't read the sequences as big numbers, but rather a sequence of one digit numbers without spaces. And the last number (digit) of the last sequence (of 1 digit numbers) of the infinite whole sequence, is 1 because it always is 1 and it can't be anything else than 1.
But they not ask for the number (btw a Conway sequence), but "Can you figure out ...". So the answer must be "yes" when you can, otherwise "no" when you can't.
that video is
95% childhood trauma
4% gaslight sold as “thinking out of the box”
1% maths
Is there a rule of the internet that "there's an XKCD for that?" Because I entirely agree with what I think is Tom's main complaint and the same as Randall Monroe voiced 18 years ago in XKCD 169: "communicating badly and then acting smug when you're misunderstood is not cleverness."
And for my less TL;DR commentary:
#2: The order of operations "riddles" are so common online that this should be pretty easy. Note that it also highlights why BODMAS (or PEMDAS) doesn't even work: after M, you have 3+9-3+3; applying A next gives 12-6, which is 6. To get 12 you have to either use BODMSA or group as BO[DM][AS] or PE[MD][AS], applying addition and subtraction together.
#3: I got "2, but they're going to tell me it's 3" because I think embedding maths notation implicitly groups that apart from the operations in the English text. At best, it's ambiguous (unlike #2, which is well-defined because it's all written in symbols).
#5: The answer just straight-up lied about what the question was, so the video can *&^% right off with that one.
#6: I see Tom missed the extra instruction "all you can use is addition" because it was spoken but not on the board. Which actually helps because the only thing you could use and then pretend is nothing is writing multiple 8s as one number. And then there's barely enough time to say "888 leaves 112, so plus 88 and plus however many are left as singles and I hope that works."
#8: Tom's attempt imaginines extra '+' signs between the lines. I got to "do they want to ignore the first two lines and get 2 or join them into 1+1+1+1+11+1+1+1+11+1×0+1 = 30?"
#9: The Look And Say Sequence is pretty instantly recognisable to sequence fans. Find it as OEIS A005150.
For #6, I did 8+8+8+8+8+8+8+8+936. They never said we have to ONLY use 8.
I did (8 × 8 × 8) + (8 × 8 × 8) - (8 + 8 + 8), then realised I used nine 8s. Degree in pure maths and I can't count to nine, apparently.
@@hughcaldwell1034 ((8*8*8)-8)*((8+8)/8)-8
@@hughcaldwell1034or hear either apparently, it says you can only use addition😂
@@peterb5 The part about only using addition was the only way I got it quickly. You need 5 8's in the units column to make 0, carry 4. Then 2 more 8's in the tens column for 0, carry 2. Then 1 more 8 in the hundreds column for 0, carry 1.
@@peterb5 Oh damn... Yeah, really glossed over that one... I'm used to encountering variations of this question with a pretty standard stipulation that the four basic operators are allowed. I was mostly watching for the commentary anyway, though, since these types of questions are usually irritatingly trivial or just badly phrased.
#3 they clearly got wrong too. In mathematical writing it is completely standard that a formula surrounded by text is treated as a whole. You never have a part of the formula interact with the text, and then with the rest of the formula. So the answer is unequivocally 2.
My instinct was that the answer was 2, but realised it was too obvious, so re-read it to come up with the 'right' answer. But it just didn't 'seem' to look right, but I couldn't understand why. Sure, if you follow BODMAS, the answer is 3, but as I read the question, I couldn't see whatever seemed wrong with it.
Your explanation makes it so clear, so thank you for putting me out of my misery!
Yup
As a PhD. from Oxford (or Cambridge) you should know that there is a convention about precedence of operations: multiplication precedes addition: a+b*c = a+(b*c) and not (a+b)*c, this is not left to what one "wants to do".
Exactly I’m still in high school and it baffled me how he got this wrong.
A pHD student is not going to waste their time with arithmetic rules. Tom probably hasn’t done a calculation like that in years!
Oh, I at first thought he meant that (a+b)c=ac+bc.
I mean (a+b)c is equivalent to doing addition first and then multiplication, and ac+bc is equivalent to doing multiplication first and then addition.
On the other hand, this property has little to do with the example in the video, so you’re probably correct 😅
He should have known that but I also agree that when you are communicating maths you wouldn't write it in that way precisely because it confuses rather than illuminates what you are trying to convey.
@@lustrous3846thats bs. Its basic math, you dont need to do exercise
for 1+1+1+1+1 question, there is no operation between the lines (no hanging +), so they are different independent statements and have no bearing on the last statement. The last question is a description of the digits in the previous number in the sequence. 1 is described as "a single one" aka "one one" aka 11. 11 is described as "two ones" aka 21, then "one two, one one" aka 1211, etc... Numberphile did a video on it.
Wrong. No hanging + means concatenation is implied hence 2 eleven and the answer is 30.
I do agree with Toms statement that riddles like these abuse math to wrongly make people think math is hard, and that this is a bad thing.
I'm pretty sure the answer for #8 is a vector (5 5 2) since there are no symbols uniting the lines
I originally got 12, and then quickly changed my answer to 30 after I saw they had omitted the missing plus signs on the end of each line. I thought they maybe wanted you to concatenate them to make two 11s, but apparently not 😂
But you have no = signs after the first two lines, so clearly you are not supposed to give an answer to these.
@@general_isaac I did the same thing, 30.
@@general_isaac forgot the x0?
There are no symbols that join them in a vector. But in any case, it looks vertical, it would be a matrix with 3 rows and 1 column.
my answer was
5
5
...=2
No connection seen between each row.
The last question - key is to read the numbers aloud to get the next number - the first number is one one - 11 (which is second number) - so the third number is two ones or 21 - which is one two then one one etc
you’re a fucking genius my friend. bes wishes buddy you going far for real
Yes. However I don't think there's a clear end via this algorithm.
You can interpret the question "can you take 1 from 19 to make 20" as "make a correct expression out of 19 - 1 = 20". You could say 19 - 1(i^2) =20
I have found the answer for the question left opened.
And i have a Formula in getting what i got
The answer is
13122111
And the cornerstone of the sequence is 21
And my formula i used to get my answer which proves the results of the previous group of series before the expectant is binomial triangle method but with a little bit of complexity in it.
The final one is just a matter of reading out and counting the numbers of the previous sequence.
The first is one 1 (written as 11), next is 2 ones (written as 21), then one 2 and one 1 (1211), and so on. So the answer is 13112221. It's actually an interesting analogy to file compression algorithms :)
I really dislike these as a concept. Not the riddles themselves, but the whole "thing" around the riddles. The poorly written prompts, grammatical errors, taunting phrasing. Everything about these riddles feels like they're designed to prey on people who are easily influenced. They fish for engagement with every single aspect of their presentation.
I think there's a bigger mistake these riddles make: the answer to a riddle should be fun even if you got it wrong.
For anyone curious, the trick to the last riddle is to express the previous term in words and interpret that worded expression literally as the next term in the sequence:
1 - first term
11 - "1" has one 1 (one 1 = 11)
21 - "11" has two 1's (two 1 = 21)
1211 - "21" has one 2 followed by one 1 (one 2, one 1 = 1211)
111221 - "1211" has one 1 followed by one 2 followed by two 1's (one 1, one 2, two 1 = 111221)
312211 - "111221" has three 1's followed by two 2's followed by one 1 (three 1, two 2, one 1 = 312211)
So the next term would be 13112221 because "312211" has one 3 followed by one 1 followed by two 2's followed by two 1's (one 3, one 1, two 2, two 1 = 13112221)
I've seen #8 multiple times online, and there they say that since there is no + in between the 1 at the end and the beginning of a row, its 11. So you basically add 4 + 11 + 3 + 11 + 0 + 1 = 30. But yeah.
That's what I got.
You can't just ignore the carriage return. How does that in any way make sense? It's clearly 3 unrelated lines, specifically 2 expressions, and 1 equation that you need to finish.
@@TahgtahvWell it makes sense if you just run out of space and have to continue somewhere.
For problem #2 the same applies in programming. Programing languages have well-defined operator precedence rules which define the order of the operations, however adding parenthesis/brackets around the groups makes it easier to read/follow, especially for complex equations or logic checks.
18:16 Well, on that one, they aren't very clearly part of the equation. There are not math operators linking the first two lines to the last. The answer I got was a 5, another 5, and a 2.
You're missing the point. Due to the lack of rigor in all of the previous problems, you simply can't determine what the person who created the problem intends, because anything is acceptable if it leads to more people getting the answer wrong.
I understood it as the last one from one line and the first line from the next line as 11, so the answer as 30
@@weirdlyspecific302 What the person intends is not relevant to my comment. Tom says the numbers are "very clearly part of the equation" and I'm saying that, because of the very lack of rigor you refer to, they are *not* _very clearly_ part of the equation.
@@GeekRedux you are right.
The only thing that surprised me was the reaction to bodmas. Can you imagine doing algebra without bodmas? 5 + 3x would equal 8x if you just go from left to right. Having to write 8 + (3x) would be so stupid. And if algebra becomes tedious and difficult without it, every other part of maths would too because it is literally built on algebra.
Last one was especially non-math, the answer is 13112221: the previous number has one 3, followed by one 1...
There is actually a fairly interesting bit of mathematics related to the "look-and-say" sequence. John Conway showed that the ratio between adjacent terms approaches a constant, and gave a polynomial with integer coefficients, of which said constant is a root.
The sequence ends in a repeat: the same number will start appearing because it describes itself
@@remischmitt9308 This is not true. The sequence grows (asymptotically) exponentially forever. The only starting number which results in a sequence that doesn't grow infinitely is 22, since that stays at 22.
@@remischmitt9308it's provably nonrepeating in the strict sense, i.e. it's nonperiodic. sure you'll see the same patterns reappear, but they will forever do so somewhat randomly.
50% divided by 2 can't be 1, since they never say that it's 50% of 1. So since it's not 50% of anything specific, but 50% in general, the answer is 25% of that thing that we don't know of.
If we were to accept that it's 1/2, we get 1/2 divided by 2, which is 1/2*1/2 = 1/4
Also, it's not 1/2/2, but rather
They want you to assume that it is already half of 100% so it is already divided by 2. This question is written wrong for the type of answer they are looking for.
Wait are u guys seriously thinking number 5 is wrong
50% ÷ 2
50% = ½
½ ÷ ² the number two's cancel each other so 1 is left
But for using decimal i have no idea
When I first noticed these 'order of operation' type riddle short videos, they were almost always about fighting over notation; as if there somehow was ONE correct interpretation. Often the parties arguing genuinely did not know better, as they had their particular 'correct' notation drilled into them at school over and over again (and had eventually given up resisting). Now we have math professors join in and tell what we (the non-resigned) knew all along: The notation means what we agree the notation means, and if there is doubt we should really agree ahead of time. So, rejoice, math fans, we won! (thank you Tom).
The thing about any expression is that it is attempting to express something. So the correct answer to "3+3x3-3+3" and its friends is always "Express yourself more clearly!"
@@peterbrockway5990 I find that often there is some context present, like a particular computer language or a particular math model problem, that will make the expression fairly well-defined (I guess 'fairly well-defined' is an oxymoron). The 'fun' or 'riddle' part is to some extent that the context is removed. Would it help if I go, say, "(3 + (3x3) - 3) + 3"?
I am happy to go along with "3+3x3-3+3" when I feel I know the context. Are you more stringent, to the point, where you would still go "express yourself more clearly" even if you think you might be able to guess from the context?
To me the win in this video is that WHEN the context might not be clear, or maybe entirely missing, THEN the expression defaults to largely undefined (or "bad notation" in Tom's words).
I didn't see any comments on puzzle #8 but the first 2 lines are not part of the equation because they don't have a plus sign in the end. Completely legit, very subtle trick.
have you ever seen numbers written on multiple lines? Like long expansions of decimals of PI where you continue the digits on the next line because there isn't enough space on the first? 1 + 1 + 1 + 1 + 11 + 1 + 1 + 1 + 11 + 1 * 0 + 1 = 30, those pesky 11's clearly take up so much space on the blackboard they had to be split on multiple lines, much like PI.
13112221. Read the numbers. There’s 1#3 1#1 2#2’s 2#1’s.
Go back to the lines starting from any eg 1211 next is 1#1 1#2 2#1= 111221
#3 depends on how you read the problem. If you pause after "half of" then in constant speed say "2 + 2" then the answer is 2. But if you pause after "half of 2" then and "+ 2" then the answer is 3.
The problem with word problems in math is that they are ambiguous and depends much on both context and how it is interpreted.
Tom , do we have Oxford university mathematical papers from previous decades, centuries ??
There is something so pleasing about seeing a maths professor get as frustrated with these videos as me! 😂
I also made the exact same mistake as you on #6…
20:05 13112221 basically saying how many numbers there is like 1 how many ones one like one 1(11) then how many ones(2)(21) so on didn't copy pls don't attack ke
Okay so question 3 doesn't make sense. By order of operations, you do parenthesis first, and switching notation (from linguistic to mathematical notation) it's grammatically implied to be separated ideas
20:24 It is the “look and say” sequence (it’s called something like that) and the next term is given by saying the number of a certain digit in order so the next one will be 13112221
I'm MSc math and do not always respond correctly to riddles, even though I've constructed some crazy (correct) proof's over the years. Now I feel better.
For problem #8 you have to ignore the two first rows because there are no functions between them. Even if you don't want to ignore them, you don't know if your supposed to add, subtract multiply or divide or what you're supposed to do, cant just assume that you're supposed to add it when it doesn't say so.
18:00 the answer is actually 30! Notice how the second and third row end and start with a 1 respectively. same thing with first and second row
I'd say only the '50% question' is a legitimate logically wrong question, the rest are valid. Since it's riddles and not straightforward questions, the roman numerals question is definitely valid. And the one where they said the first 2 rows aren't the part of the equation is also correct since they didn't have any symbol at the end of the lines or at the start of them.
About the last one, I'd say the answer is infinity since they said 'the last number in this sequence' and the sequence is divergent.
I already learned the trick to the last question but... Every time I see a question like this it reminds me that any finite series of numbers can represent the values of a carefully-chosen polynomial. Which values? Could be solutions for P(x)=0 or P(1),P(2),etc..
That last / bonus question likely doesn't have an end. You're basically saying how many digits of which digit as you read the number left to right.
1
One 1 -> 11
Two 1 -> 21
One 2, one 1 -> 1211
One 1, one 2, two 1 -> 111221
Three 1, two 2, one 1 -> 312211
Going on like this, I don't think there's a defineable end. However, if you were to go with the total number of a given digit in the order those digits appear, you do get a defineable result:
1
One 1 -> 11
Two 1 -> 21
One 2, one 1 -> 1211
Three 1, one 2 -> 3112
One 3, two 1, one 2 -> 132112
Three 1, one 3, two 2 -> 311322
Two 3, two 1, two 2 -> 232122
Four 2, one 3, one 1 -> 421311
One 4, one 2, three 1, one 3 -> 141231
Three 1, one 4, one 2, one 3 -> 31141213
Two 3, four 1, one 4, one 2 -> 23411412
Two 2, one 3, two 4, three 1 -> 22132431
32212314
23322114
32232114
23322114 which we've already done; we've hit a repeating loop.
"Can you figure out the last number in this sequence?"
You got the rules wrong. The next on the sequence is 31112221. It is obvious it always ends in the number 1. So even if you go to infinity the last number is always 1.
@pulsar22 That's the first paragraph: I don't think there is a last value. I did figure out that you say how many of which digits (consecutively) there are followed by the digit in the order they appear.
1
11
21
1211
111221
312211
13112221
1113213211
31131211131221
13211311123113112211
11131221133112132113212221
3113112221232112111312211312113211
1321132132111213122112311311222113111221131221
See what I mean? It seems to keep going and going, never getting to a repeating point. If the question had asked what the *next* value was, I agree with you. It's an improperly asked question, like that "50% divided by 2" one.
@@pulsar22 they asked for the last number, not the last digit of the last number
Bodmas doesn’t apply to a sentence - it applies to mathematical notation. Once you describe the problem in words, the rules of verbal interpretation apply.
Brightside came up on my feed and was blocked after watching a video. I appreciate you doing this. Their videos are crap.
#8 you could argue 2 solutions
Either consider that the first 2 lines are not part of the equation since there's no + sign at the end, which results in 2.
Another way to look at this problem is the coding grammar where spaces within an equation are first trimmed and we get
1+1+1+1+11+1+1+1+1+11+1+1x0+1= 32
Thanks Tom, these daft problems seem to pop up more and more regularly.
The 1+1+1… turned out to be 30… the lines wrapped around and there were two elevens in the middle of the list. One of the 1’s was multiplied by 0 so it disappeared. If I subtotaled, it would look like 4+11+3+11+1.
19:37 it was not part of the equation because the second and third line did not start with pluses, neither the 1st and 2nd lines ended with it
Riddles, when applied to certain disciplines, are frustrating. "Math riddles" are meant to trick you into applying that mindset to it. Question 8 uses it well. "The indented portion wasn't part of the equation." Where plenty of others have stated that's not normal mathematical practice.
12:29 The Oxford math professor outsmarts the Bright side writers, that is what I came here to watch!
On #6, I did:
8/8=1
8-8=0
8-8=0
8-8=0
Concatenate the answers, 1000.
My dumbass did 8+8+8+8+8+8+8+8 converted to base 4
For the 50% question, I think what they did is that since 50% is (50/100), they divided that by 2, i.e. 50/100/2 and the 50/100= 1/2 and since there was a 2 dividing (50/100) it would go in to the numerator making the eq look something like (1/2)×2, the two in numerator will cancel the 2 in denominator resulting in 1.
Nah bro ur dumb
For #8, even if you consider the first two lines part of the equation, it's still not 12. There is no operation between the end of each line and the beginning of the next. So yes, they are trying to trick you, but also no, it is not clearly one equation.
I was able to do #6 in the allotted time, but only since I had some experience with these videos and know some of the patterns in their answers. I also had to use some weird tricks to find the answer quickly.
First I asked, “how could adding 8’s give us a 0 in the one’s place?” The only reasonable answer is by adding 8 five times, which would give us 40.
I could then use similar logic to set the other digits to 0. I thought “how many times do I need to add 8 to the tens place to turn the 4 in 40 into a 0?” Well, twice because 8 + 8 + 4 = 20, so 80 + 80 + 40 = 200.
Lastly, the hundreds place needed one 8 added to the 2 from 200 to set the digit to 0. 8 + 2 = 10, so 800 + 200 = 1000.
Then, to get rid of the zeros in our numbers, we replace them with other 8’s. So long as we add one 8 in the hundreds place, 2 in the tens, and one in the ones place, we’ll get 1000. That’s how we get 888 + 88 + 8 + 8 + 8 = 1000.
the#5 may have something wrong, because 50% decided by 2 is obviously = 0.25(25%)in any way although 50%=1/2 and we use 1/2/2 =1/2*1/2 =0.25
What I interpreted for 50% divided by 2 :-
50%/2
50% means 1/2
So substituting 50% by 1/2
We get,
1/2/2
Which can be written as
2/2
=1
I know this is wrong but this is what I got 😅
RE: order of operations
The order we have exists because algebra is easier to do if you don't need brackets everywhere to make it clear 3X+5 means (3×X)+5 rather than the unintuitive 3×(X+5).
Their teaching as a rule to kids who don't understand the reasoning is IMO part of the problem with the whole education there. No one writes such problems with numbers for anyone over 8 or 9 because by that time you're getting introduced to the basics of algebra and it stops being an issue.
Tom, with question 8, you failed to notice that there were no addition signs at the end of the first to lines to connect the three lines together as one equation. Hence, the video was correct with that question. I do, however, agree with you regarding question 5, he clearly said "divided by 2" not "divided by half".
#7 can be solved differently
If you take 19 in base 10 and substract 1 you'll get 18 which 20 in base 9. I find this solution to be more rigourous and more mathematically correct
The last one is the Conway sequence, I had a coding test on it a few days ago so I definitely remember it :)
So here is my thought for #5....
if you divide any number by 2 then it means that what we will be getting is the half of that number....
For example if you divide 10 by 2 then its the half of 10 i.e 5.
But i guess they rather divided it by 1/2 thinking that it would give half of 50% but they actually had to multiply it by 1/2.
that's where they got it wrong... what do y'all think
Tom doing %50/2=%25 is utter nonsense
%50= 50/100 which is 1/2
1/2 divided by 2 is= 1
Problem 2 is a matter of operator precedence rather than order. All operators with the same precedence can be evaluated in any order. In this context, infix operators are assumed.
Polish and Reverse would be much better : bracket free.
50% divided by 2 is 1 if you look at it like (1/2)/2 which gives you 1 after moving the bottom “2” to the top
you have to count the number of digits:
1
11
21
1211
111221
312211 (3 ones, 2 twos, 2 ones)
The 1+1 and so on-equation is very clearly 2. There's no mistake, just confusion. On the new lines it doesn't start with '+'. That's a dead giveawey.
The last one are just the look-and-say numbers.
I can accept that at the "puzzle" level Roman numerals are used and even a vague operation like "take" (removing a symbol) is an option.
But, reciprocally and for consistency, I hope that all my answers that use these tricks will be accepted as valid.
That is, I have the freedom to solve in other numerical bases, in other arithmetics (modular for example) in other languages, operate according to the meaning of the dictionary... and in general, jump freely between different rules that were not specified.
For #8, I was taught at school that if you have to change lines in an equation you need to say what are you doing next and follow it to the next line.
Like in this case:
1+1+1+1+1+
+1+1+1+1+1+
1+1x0+1
If it would be written like this then 12 is the correct answer.
At least from what I was taught
That would double the plus signs. Now for plus signs this doesn't pose problems, but it would if you do this with minus signs.
4-
-2
is actually 6, because it says 4 - -2.
If you continue a line, just write the operator at the end of the first line:
1+1+1+1+1+
1+1+1+1+1+
1+1*0+1
or, preferably, at the start of the next line:
1+1+1+1+1
+1+1+1+1+1
+1+1*0+1
The last is prefered because here too, if the line were broken at a subtraction, then the minus sign would be close to the subtracted number.
For question 5 the answer is one because 50% is 50/100 if we divide that by 2 then we will get 50/100/2 which we can do 2 ways we can just divide and get 50/50 or we can multiply 2 with 50 and divide it by 100 = 100/100.
I agree, bad notation is bad! However most people who "understand" PEMDAS (or any variation of it) assume a logical order as follows. Left to right order because it's how we read (in English). A lot of people don't know that [M and D] and [A and S] have equal priority. Then, within that priority bracket we apply left to right logic. So for example 2(3 + 2)^3 = 250 because brackets/parentheses --> orders/exponents/powers --> multiplication. Alternative "solutions" may be 70 or 1000 but even with brackets here, it's not "obvious". My answer to the last question with way more than 15 seconds is: 131112121111 but it think that sequence is just - say what you see in the last sequence in words. Less than 1 min. Am I smart? Maybe? Dr. Tom Crawford is miles better than me at mathematics. I think the issue with people in extremely high academic standings is that they lose track of the basics when working on REALLY complex problems! I admire them greatly though!
Correction: 13112221, silly sequence but I was wrong.
I'm surprised Tom (nor the video) did not know about the "look and say sequence" (studied by Conway) which provides the answer to the last question.
For number 8: They aren't just arbitrarily ignoring the first 2 lines. There's no addition sign connecting the first 2 lines to the equation.
I don't really like BODMAS or PEDMAS. I think it's wrong to imply that Division should be resolved before Multiplication and Addition before Subtraction. It may seem pedantic, but honestly I think it can cause confusion later in math. The students I've tutored seem to get this idea that Division and Multiplication (or Addition and Subtraction) are somehow fundamentally different from one another. Yes, they are technically different, but the difference is analogous to walking towards vs. away from something - you end up in different places, but in either case you are still walking (i.e. the action is the same).
IMO it would be better to teach students that order of operations is about identifying parts of an equation (e.g. what are we trying to multiply? what are we taking the logarithm of? what are we adding together? etc.). Once you can identify the parts, order of operations becomes irrelevant. So long as you're consistent in the "what" of each operation, the math will always work out.
Yeah I guess if people rely only on the order of letters there and forget it's meant to be like PE(MD)(AS). I guess it could be simplified as PEFT for parenthesis exponents factors and terms? I may have an unpopular view on this but I'd go as far as to say there's no difference between addition and subtraction, and that it's a mistake to think of them as operands acting on two values. If you view the expression 3 - 4 as two terms, +3 and -4, suddenly the order doesn't matter despite it being subtraction (3 - 4 isn't 4 - 3) but the terms +3 and -4 evaluate to the same as -4 and +3, so 3 -4 = -4 + 3. I believe this way of thinking is commonly used already when simplifying expressions. Like 3 + 4 + 5 - 4 = (+4 and -4 cancels out) = 3 + 5, suddenly here we don't think of the - as an operand acting on 2 values. The exact same goes for factors, apart from rewriting 3 / 2 as /2 * 3 isn't exactly standard notation, but personally I think it makes sense.
Edit: I say no difference, but obviously subtraction means the next term is negative. My point it wether it's addition or subtraction it's just a list of terms that have to be evaluated, positive or negative.
That "what is 50% divided by 2" one was stupid. They blundered - no marks to them for that one. A good time to exit.
For the 1+1+1+1+1etc question, i assumed that the 5th and 6th, and 10th and 11th 1's were actually an 11 since there was no sign noted between them. Doing this I got an answer of 30.
1+1+1+1+11+1+1+1+11+1×0+1=30
For #6, there is another more likely to be a math solution.
[(8 + 8) * 8 - (8 + 8 + 8) / 8] * 8 = 1000
8 + 8 = 16
16 * 8 = 128
(8 + 8 + 8)/8 = 3 * 8 / 8 = 3
128 - 3 = 125
125 * 8 = 1000
For #9, the "last number" is ambiguous. The sequence can continue forever, so you cannot say that a number is the last number, in mathematical sense.
Hey Tom! Idk if you’d be interested in this but the LSAT just removed their “logic games” section from the test, which tested lots of conditional logic. Would you consider doing an LSAT Logic Games section? Think it would be really cool to see! Keep up the good work on the vids
the one with all the ones is definitely 2 after looking back because at the end and beginning of each line there is no function so they can't be a apart of the same equation
Omg, i can't believe they don't have answer to #9.
It's one of my favorites.
It's 13112221.
You almost had it when you said counting the ones. Each is count the amount of numbers in the previous.
One,
one one,
two ones,
one two and one one,
One one and one two and two ones,
Three ones and two twos and one one,
Etc
they have the answer, they just say it like that to bait people to engange in comments since it helps the video
The original video being reacted to should have been called "How to make a mathematician salty in nine easy steps"
What is 50% divided by 2.
Think out of the box:
There is another meaning to the sentence:
(What, divided by 2, is 50%)
=> What becomes 50% when divided by 2. => ans: 1.
The first one is 50% / 2 = x And the second one is x / 2 = 50%.
X1 = 25%, X2 = 100%. You can figure it out yourself tbh.
"What, divided by 2, is 50%", is the same as --->
X, divided by 2, is 50% -->
X / 2 = 50%
X = 100%
for problem 6 i got
sqrt(sqrt((8+8+8+8)^8))-8-8-8
My guess for #8 was 10. I knew _something_ was up without the plus signs, but from there, it was impossible to guess exactly what we were supposed to do. Since two numbers next to each other typically means multiply, I assumed the 1 from the previous row was supposed to be multiplied by the 1 from the next row, which going by PEMDAS, would equal 10. So yeah, there's no way to get that right without either getting lucky or being a mind reader, because even noticing the missing plus signs, I wasn't sure what the cartoon teacher wanted us to _do_ with that information.
the 8 eights question, (8*8*8)+(8*8*8) gives 512+512 = 1024. log 2 8 and multiply that by the remaining 8 is 3*8 = 24 . 1024-24 = 1000
But the log 2 requires a 2, which isn't allowed (only 8s!), * (multiplication) isn't allowed, and the 1024-24 is a subtraction, which also isn't allowed (only addition can be used, if you listen to the original question).
@@gary.h.turner they didnt say only 8s. They said only additions
@@Mimik9X00 I admit the question didn't actually specify "only 8s", but if it had meant "eight 8s, together with ANY OTHER numbers you want to use", then there would be a huge number of solutions, which wouldn't make for a very interesting problem!
Number 4 is wrong, even if you turn 50% into 1/2 you get (1/2)/2 which is 1/4 because it is the same as (1/2)(1/2)
6:00 when i was a wee little lad in school they taught me PEMDAS or BEMDAS (their quite similar) parenthesis exponents multiplication division addition subtraction.
love how number three frogets proper grammar tho
actually, 3+3×3 is quite clear because it didn’t have brackets. It’s obviously the multiplication that should be perform first it is just you who confused the order between multiplication and addition
In fairness the 1+1+1+1+1
Has no continuing operation after the fifth one on the first line or the second line
Is it half of 2... plus 2 (three). But I clearly heard "What is half... of 2+2" (two). These kind of interpretive questions are REALLY maddening because both answers can be correct depending on how you ask the question.
13112221.
Each number describes the previous number. 1 has one 1. 11 has two 1s. 21 has one 2 and then one 1. 1211 has one 1, one 2, and two 1s. etc.
#7 first two lines are not part of the equation because there are no connecting operator between line 1 to line 2 and from line 2 to line 3. If you are a sharp computer programmer you would notice this immediately because what is written on the board would give a syntax error.
7th riddle is actually very easy ,because they're asking a yes or no question, and based on the previous riddles what they mean is how do you do it, but that is not what they wrote. and by that logic you can with good confidence just answer yes without even knowing if its right or not.
13:38 If you think of it as just the number 8, there is still a way to do it.
(8+8)×8 = 128
(8+8+8)/8 = 3
(128-3)×8 = 1000
Nice! I couldn’t find a solution that didn’t use seven 8’s 😅
The voice over did say you could only use addition even though that was not written on the screen, so whilst your answer is valid if other operations other than addition were permitted, it is not when addition only is permitted. Also to present you answer you had to use the digits 1, 2 and 3. The question clearly said to use only 8's.
Also, 8*8*8=512
512-8=504
(8+8)/8=2
504*2-8=1000
or (8*8*8-8)*(8+8)/8 - 8 = 1000
@sebastianpersson104 you too must have missed where the voice-over said only addition was to be used.
I think that the 'problem' with a well qualified mathematician attempting to solve these puzzles is that 'proper' mathematicians look too deeply in to them for an answer. I'm an accountant, so good at 'simple' maths, but I wouldn't call myself a 'mathematician'. For the '1000 using eight 8s' puzzle, the instruction that 'addition' was the only operation allowed, i quickly deduced that you need to add five numbers that end with '8' in order for the last digit to be zero. So now I have three 8s left. 88 + 88 + 88 plus two eights will be nowhere need 1000, so one number must be '888'. Then I've only got one more '8' to 'play with', so there must be an '88'. A quick check shows this must be pretty close and is the only solution that is, so must be the right one. So it is possible in 15 seconds.
Each number in the last question describes the order of digits in the previous number, so the '11' given as the second number isn't 'eleven', but says 'One 1' (because the previous number contains one 1, but no other digits). The fourth number (1211) effectively says 'One 2, One 1' (explaining the '21' given just before). So the first missing answer is 'One 3, One 1, Two 2s, Two 1s' (13112221).
I didn't get the Roman Numeral question right, but would agree that although 'BODMAS' or 'PEDMAS' is taught in school, puzzles involving orders of operations could often be notated better.
Thanks for making this vids the fault isn’t on you, If I did these problem I’ll be more angry it not math anyway, your math skill is really great.
18:15 I mean they are not part of the equation, the lines end in 1 not plus sign right? so they are by themselves
Can you solve ted ed riddles?
hmm 50% divded by 2, so that would be 1/2 over 2/1 so that goes to 1/2 * 1/2 = 1/4.
the last one is actually a clever sequence i'd gotten acquainted with decades ago. i call it the "whatchu got?" sequence ...or the "read it back to me" sequence. it goes like this: start with 1:
1
"ok, whatchu got?"
"i got one 1."
11
"whatchu got now?"
"two 1s."
21
"now whatchu got?"
"one 2, one 1."
1211
[...] "one 1, one 2, two 1s."
111221
312211
13112221
1113213211
.
.
.
it has i don't know its oeis#, but it has a fancy name. last i checked it had no explicit formula, but many papers have been written about it, several standing/unresolved/unproven conjectures.
it resembles a fractal... a 1-d aperiodic tiling...
does anyone know if a 4 (or anything other than 1, 2 &3) will eventually crop up?
10 is the "say what you see" sequence. 1 is one 1. (11) i see two 1s.. (21) i see one 2 and one 1 (1211) the answer is 13112221
I actually got #6, but wasn’t 100% certain I was right in the time. They said using only addition, so I figured concatenation had to be legal. We were never going to get anywhere near it if we didn’t do 888. This leaves us a bit over 100 away, and they told us it was 8 8s, so I figured it was 888 + 88 + 8 + 8 + 8, because 888 + 88 + 88 + 8 would over shoot, but I was still working out if it was exactly 1000 when time ended.
17:55 you could get another answer
Those 2 1 can become 11
So it could be 30 as an answer