I'm sorry but this is not a logic test. by labeling it as a logical test, you mislead people into solving the problem outside the conventional mathematical paradigm and into finding some different correlation between the numbers which are not related to direct, obvious computation. this problem should have been labeled as: _solve the following mathematical equation_ .
The question was: Can you solve this logic puzzle? 2 things: it’s considered logic and a puzzle! Two things that are not necessarily genius. Anyone should be able to use basic logic or any other unconventional method to solve it.
You can in fact use a certain amount of logic here. We are told that x ⊕ y = ax + by + c, which is linear. Also notice that in all examples, x and y have a linear relationship: y = 2x−1. As x increases/decreases by 1, y increases/decreases by 2, so x ⊕ y should increase/decrease by a+2b which is constant. Since the difference between 4 ⊕ 7 and 3 ⊕ 5 is 14, than a+2b = 14, and we get the following pattern: 4 ⊕ 7 = 30 3 ⊕ 5 = 16 2 ⊕ 3 = 2 1 ⊕ 1 = −12
Forgive my ignorance, but how do you know what to multiply the original equations by? In this case you choose 3 and 2, but why those numbers? Is it just any random numbers as long as you keep the equations equal?
I've also found a simple solution: (3+1) x (5-1) = 16 (4+1) x (7-1) = 30 So... (1+1)x(1-1) = 0 Of course we can create any logic to associate the number... but I liked this one
The way I solved it was I looked at it as a simple function. Before 3+5, you'd have 2+3, then 1+1. And subtract 14 as it goes down. And that still gives me -12.
If you write out your approach as: 4 + 7 = 30 3 + 5 = 16 2 + 3 = 2 1 + 1 = -12 the pattern is obvious, and also linear, so must correspond to PT''s answer, which assumed a linear solution. Just much easier.
Totally how I got it in my head before playing the rest of the video. To do more formally, Eq2 - 2 * (Eq1 - Eq2) gets you there, or simplifying, -Eq2 - 2Eq3 => a + b + c = -12.
The question in the thumbnail was way more open-ended. For example floor(mean(x,y)^2) satisfies the first two equations, and so 1+1=1 would be the third.
@@pedroafonso8384 he does that a lot where the thumbnail seems different/easier than the actual question. In his defense some questions are too long to fit a thumbnail but this one wasn't imho.
I must know a different version of floor and mean functions... Mean(3,5) should be (3+5)/2 = 4, and floor(x) should go to some rounded value, usually nearest whole number less than or equal to the input, meaning floor(mean(3,5)) would be 4, not 16... What definitions are you using such that floor(mean(3,5)) = 16?
@@Vertraic I totally forgot to type the squared part, thanks for double checking. Ijust edited to add that. In your version of the mean() function for whatever reason you decided to do integer division by 2 which also is a mistake.
@@Gideon_Judges6 is integer division a mathematical concept or just a computer concept? cause i don't remember them teaching me (5+3)/2 was integer division in grade school haha
There is infinate solutions, but I assumed the solution was a whole number so I got a result: a=2, b=6, c=-20 ... and it was correct (this is one of infinate solutions, but they all follow the same logic so if you get one of them u have solved the problem)
goldfndr the a, b, and c values need to work for x=3 y=5 and result=16 though. Otherwise it would work with literally any set of 3 numbers that adds to -12.
I was thinking that x and y were getting closer together in value and multiplied. If x=/=y, subtract 1 from the larger number and add 1 to the bigger number. Then multiply. 3 1×1=1 With a simpler rule set you would have gotten the last row to be 1+1 × 1-1 = 2×0 = 0
Another way to solve it as follows A. 3x + 5y + c = 16 B. 4x + 7y + c = 30 Now substruct A from B will get C. X + 2y = 14 Now multiply A by 4, and multiply B by 3, will get D. 12x + 20y + 4c = 64 E. 12x + 21y + 3c = 90 Now substruct D from E will get F. y - c = 26 Now substruct F. from C. , will get x + 2y - ( y - c ) = 14 - 26 Or x + y + c = 12 This is all
Yay! This is the first MindYourDecisions problem I solved correctly It's just a basic exercise in linear algebra. With the first two equations, I created an augmented matrix and did row reductions. Obviously, c will be a free variable; that means that the solutions to a and b will be written in terms of c. Set the solutions to a and b equal to each other and solve for c. Put the value of c back into one of the equations and you will get the value of both a and b because we just found the point where a = b. Now we have a, b, and c so just add them up since the coefficients equal 1
I've seen a lot of tests in which "c" is not constant throughout the expressions but it lineary increases according to the position of the expression. So in this case you would have a1 * b1 + 1 a2 * b2 + 2 a3 * b3 + 3 and so on. When such tests have a multiplicity of solutions they are either malformed or they just need more example cases to constrain the possible answer.
The answer to this problem depends on how you define ⊕. You do indeed get -12 with your linear algebraic definition, but other solutions are valid as well. In addition, I prefer a more systematic approach, however, such as doing matrix reduction on the 3 equations. You end up getting b - c = 10 - 4k/3 and b - c = 8 - 3k/2, where k is a constant solution for 1 ⊕ 1. Therefore, the only way for the system of equations to have a solution 10 - 4k/3 must equal 8 - 3k/2. After solving for k, k= -12.
If the relationship between x and y is not given, then it can be any relationship you want. There was no relationship given in the thumbnail or in the "logic and intelligence tests that spread across social media" until _Presh stated that the puzzle was _*_based on_*_ a well known relationship, and then went on to solve _*_that_*_ relationship._ Given the original puzzle _as presented_ (on social media and in the thumbnail), the solution can be any value you like - you will be able to find a polynomial function of x and y which gives the results for the two given results and gives the value you want for the third (I'm not saying it will be easy[1], just that it is possible to find such a function to justify the result). For example, if: f(x,y)=11x^3 - 79x^2 + 80y + 30 then f(4,7) = 30 f(3,5) = 16 and f(1,1) = *42* And that's the answer: *FORTY TWO* [1] actually as there are infinitely many such polynomials it is fairly easy to find one of them.
I challenge that argument and say it's 4. 3 + 5 = 16 ......(3 times 5 is 15... it's the 1st in the sequence so add 1....16) 4 + 7 = 30 .....(4 times 7 is 28....it's the 2nd in the sequence so add 2....30) 1 + 1 = 4 .....(1 times 1 is 1....it's the 3rd in the sequence so add 3.....4) The only way you can get 12 is if you are DEFINITELY given the equation (ax + bx + c)... otherwise you could never logically make that assumption to be true.. that's not how code breaking works... and I am sure there are many other methods people could come up with to solve for other variables. You'd need more than 2 examples with "answers" to narrow it down....
@@Renitky yes it's 1. But wrote [3/2] = 1 [ ] denotes the greatest integer function (In laymen's terms it means the integral value of "3/2" or "1.5" which is "1").
I graphed the two equations as: 3x+5y=16 4x+7y=30 These two lines intersect at (-38, 26), which led me to answering -12. I feel like I would get that “You used the wrong equation, but got the right answer” written on my test.
After subtracting (1) from (2) to get a+2b=14 it is simpler to subtract 3 x (1) from 4 x (2) to get b-c=26. Subtracting the second result from the first result yields a+b+c=-12.
Because it's not the actual numbers 3 and 5 or 4 and 7, rather these are variables. You adding 1 to the first equation and 2 to the second and getting a correct answer is nothing more than a fluke
The rule was given that the operation adds ax+by+c. That wasn't a tool for solving the problem, it was a constraint that is part of the question. Your method doesn't follow the rule.
A solution is only possible, in this form, because the third equation is a linear combination of the first two. Other solutions, such as the ones that come up with zero are also valid, particularly if you have been baited here by the original thumbnail!
0. An answer, or more precizely , one of the possible answers, is zero. Two upper lines satisfy the following expression (A+1)*(B-1) = C since (3+1)(5-1) = 16 and (4+1)(7-1)= 30 so (1+1)(1-1) = 0
Correct answer is 0. Let x be the first number and y the second number. The formula to find the correct answer would then be xy+x-2. Note that this formula satisfies both the given equations. So the answer is 1*1+1-2=0
1+1=? (-1) 2+3=y. (0) 3+5= 16. (1) 4+7=30 (2).......see my solution you will understand why had I typed (-1), 0, 1 and 2....Can you see the pattern? 3×5+1=16 4×7+2=30 Therefore, following the same pattern 1×1+(-1)=0
when I first looked at the thumbnail I thought it was 0 adding 1 to the first number, subtracting one from the second and then multiplying them 3@5 -> 4*4=16 4@7 -> 5*6=30 1@1 -> 2*0=0 Boy... I was so wrong...
You made this WAY too complicated. Once you have a+2b=14, just double that to get 2a+4b=28. Then subtract that from your first equation: 3a-2a+5b-4b+c=16-28 a+b+c=-12 This was is easy enough I could do it in my head in about a minute. Your waynis much harder.
I approached it thusly (I'm using "X" for the binary operator here): 3 X 5 = 3a + 5b + c = 1 X 1 + 2a + 4b = 16 (since 1 X 1 = a + b + c) 4 X 7 = 4a + 7b + c = 1 X 1 + 3a + 6b = 30 Multiply top equation by 3 and bottom by 2 to balance a & b, then subtract, leaving: 1 x 1 = -12
They are forcing you to make the arguments true in order to find the final answer of X. So, “+” might need to be a different function. Since the arguments don’t equate even with that, there must be an invisible variable of “c” in play. My process? 3 * 5 + c1 = 16 = 15 + 1, c1 = 1 4 * 7 + c2 = 30 = 28 + 2, c2 = 2 So it follows that; 1 * 1 + c3 = X = 1 + c3, Since the “c” value increases by 1, c3 must be equal to 3. So; 1 * 1 + c3 = X = 1 + 3 = 4 Thus; X = 4
Welcome to the world of abstract algebra! We might make the assumption that the + operator forms a group over the set on integers. In this case, we must verify the following properties: Closure: a+b always results in another integer. Associativity: a+(b+c) = (a+b)+c Existance of a "zero" element: For any a, there exists zero such that a+zero = zero+a = a Invertability: For any a, there exists b such a+b = b+a = zero Ordinary arithmetic has two well known groups. Addition forms a group over the integers in the way we naturally expect. Multiplication forms a group over the rationals, since we require fractions for the inverse, and we need to note that the "zero" identity is actually the number 1.
Hi! I solved it more simply. Subtracting the second equation to the first one: 4a + 7b + c = 30 - 3a - 5b - c = - 16 ---> a + 2b = 14 Then substituting it in the first equation: a + b + c + 2a + 4b = 16 a + b + c + 2(a + 2b) = 16 a + b + c + 2*14 = 16 a + b + c = -12
Another way is to substitute 1 equation from the second and you will get: a + 2*b = 14 Then substitute third equation from the first, you will get (z is answer): 2*a + 4*b = 16 - z Base on the first equation we know that 2*a+4*b=2 * (a + 2*b) = 2 * 14 = 28. So: 28 = 16 - z - > z = -12
Did you even watch the other comments in this video. I know this is not the solution of actual problem. But there is a lot of people that are explaining their own answers they thought by looking thumbnail. I thought this answer when I looked thumbnail, so I wanted to introduce my answer like others do.
@@SoloNit Actually it is not relevant to the actual problem. I did not write this comment to explain the solution of the actual problem, but only to share that there is another way to make 16 and 30 if there is no restriction from the actual problem.
From the first equation, when x=3 and y=5, we have: 3a + 5b + c = 16 From the second equation, when x=4 and y=7, we have: 4a + 7b + c = 30 We can use these two equations to solve for a, b, and c. One way to do this is to eliminate the constant c by subtracting the first equation from the second equation: 4a + 7b + c - (3a + 5b + c) = 30 - 16 Simplifying this equation gives: a + 2b = 7 We now have two equations: 3a + 5b + c = 16 a + 2b = 7 We can use the second equation to solve for a in terms of b: a = 7 - 2b Substituting this into the first equation gives: 3(7 - 2b) + 5b + c = 16 Simplifying and rearranging terms yields: -6b + c = -5 We can now solve for c in terms of b: c = -5 + 6b Substituting this into the equation a + 2b = 7 gives: (7 - 2b) + 2b = 7 Solving for b gives: b = 2 Substituting this value of b into the equation a + 2b = 7 gives: a + 4 = 7 Solving for a gives: a = 3 Finally, we can substitute the values of a, b, and c into the original equation ax + by + c: 3(1) + 2(1) + (-5) = 0 Therefore, when x=1 and y=1, the value of ax + by + c is 0.
This is absolutely the same method I used, and one far more logical for "code breakers"; but as you will see, other great methods were used to find different answers. I for one, think that using "ax + bx + c" is a terrible and arguably illogical assumption to make. It depends on if it was provided or not.
3+5 => 3*5+(1) = 16(from 3*5 15 i keep the num 1) 4+7 => 4*7+(2) = 30(from 4*7 28 9 i keep the num 2) 1+1 => 1*1+(0) = 1 (from 1*1 01 i keep the num 0) the pseudo-formula is : a+b =c =>> a*b = c (from ab i keep the first digit of the product ab ,let it be d) so "a+b" => c = a*b +d
I got -12, but find how you did it interesting. I showed that c = 0 earlier (by rearranging one equation and substituting it into another) and solved the simultaneous equations I was left with. I guess your method is better as it involves less steps.
From the thumbnail, thought the rule was: a + b = (a+1)(b-1), giving 1 + 1 = 2(0) = 0 Obviously then I realised the video had a question itself nothing to do with this
Multiply first eq by 3 and 2nd eq by 2 and subtract 2nd eq from first. 9a+15b+3c = 48 -. 8a+14b+2c =60 _------------------------- a+b+c = -12 Quicker than Presh and no Gougu theorem needed
Because that's what stated in the problem @0:14. "Suppose we have a binary operation...." and it goes on to clearly state how that binary operation is defined. How is this confusing to so many people? The problem never said to invent your own binary operation.
Assuming that linearity holds, just multiply the first equation by 3, the second equation by 2 and subtract the second from the first, i.e. 3*(3+5)=3*16=48 and 2*(4+7)=2*30=60, then (9+15)-(8+14)=48-60, so 1+1=-12.
I did it this way: first you define, as per 0:40, 3a+5b+c=16 4a+7b+c=30 a+b+c=X (we're looking for X here) Substract the first equation from the second and you get a+2b=14 Multiply that by 2 and you get 2a+4b=28 Substract that from the first equation and you get a+b+c=-12 a+b+c=X, so X=-12
I thought this was gonna be one of those viral problems where you could come up with all kinds of formulas which gives all kinds of different results for 1@1, but then the rules were more clearly explained and it turned into an algebra problem. Substitute x and y to make the following equations: 3a+5b+c=16, 4a+7b+c=30, a+b+c=? If we subtract the first 2 equations, we can solve that a=14-2b. Substituting back in to one of the equations, we can solve that c=b-26. Now if we plug those into the 3rd equation we get (14-2b)+b+(b-26) = ? The b's cancel out giving us 14-26=-12.
You can just subtract 2*(4a+7b+c) from 3*(3a+5b+c) , which is equal to a+b+c; on the other side it's 3*18-2*30, which is equal to -12 and then you already have your solution
The problem with this is, given the original question, you can find multiple patterns that give a valid answer. your proposed solution is just one assumption of many. therefor, the question itself is ambiguous (you see the same problem in some iq tests by the way).
This method is hard to understand you can make it so much easier by applying : 3x + 5y = 16 4x + 7y = 30 x + y = ? searching X and Y with elimination method ( I find it easy ) with : 12 x + 20 y = 64 12 x + 21 y = 90 and y = 26 substitute that to 3x + 5y = 16 x = -144/3 x = -38 then add those two 1x + 1y = (-38) + 26 x + y = -12 there, I know it's longer but for me it's easier to understand.
Since we get a-2b=14(equation 3) by subtracting the 1st equation from the 2nd equation, we can multiply the 3rd equation by 2 to get 2a-4b=28(equation 4). Then substract 2a-4b=28(equation 4) from 3a+5b+c=16( equation 1) to get a+b+c=-12 (Another Method)
1+1=? (-1) 2+3=y. (0) 3+5= 16. (1) 4+7=30 (2).......see my solution you will understand why had I typed (-1), 0, 1 and 2....Can you see the pattern? 3×5+1=16 4×7+2=30 Therefore, following the same pattern 1×1+(-1)=0
Did anyone point out, the problem is only soluble because the left-hand sides 3a+5b+c, 4a+7b+c and a+b+c are linearly dependent. This is because the determinant of the 3x3 coefficient matrix is zero. Given that, we know there will be a nulling vector (A,B,1) such that A(3a+5b+c)+B(4a+7b+c)+(a+b+c)=0 regardless of a, b and c. Thus 3A+4B+1=0, 5A+7B+1=0, A+B+1=0. Solve any two of these for A=-3, B=2. Then 16A+30B+x=0, x=48-60=-12.
Odd, I tried taking an intuitive approach to this 5+3=8*2=16 4+7=11*2=22+8=30 So therefore using that same logic of multiplying the result by 2 and adding the previous sum of the last pair 1+1=2*2=4+11=15
First of all I am tempted to think of addition in other bases (thus 3 + 5 = 12 in base 6, but no base could ever allow 4 + 7 to equal three times the base because 11 is not a multiple of 3.In base-8, the smallest base that can allow "7" as a digit, 4 + 7 = 15.
One way to conceptualize this would be to replace the addition sign with multiplication, and determine what missing quantity would add up to the number in question; then decrement by one each time. In that case: 4x7 [+2] = 30 3x5 [+1] =16 2x3 [+0] = 6 1x1 [-1] = 0 Another would be to add the numbers, and find out what addend is needed to produce the final result, but subtract 11, increasing by a factor of one each successive time: 4 + 7 [+19] = 30 3 + 5 [+19-11] = 16 2 + 3 [+19-22] = 2 1 + 1 [+19-33]= -12 Both of these make perfectly reasonable - but different - sequences. My point is that there are many (in fact, infinite) series that result in the same sequence of numbers - for any finite portion of a "series." There is no single answer for a problem like this. If you doubt that, check out the on-line encyclopedia of integer sequences: oeis.org/
EASIER SOLUTION: Just look at row operation trends, 3->4 has is an addition of 1, 4->1 is a subtraction of 3. Then on column 2, 5->7 is the addition of 2, 7->1 is the subtraction of 6. Thus the difference between row 1 and 2 of a given column is 1x, where x is a number you can easily find, and rows 2->3 has a difference of -3x. On the right, it is 16->30 which makes x=14. Then from 2->3, it's 30-3(14) = y and that gives you negative 12. Right it out visually it is WAY easier to solve it like this. 3 5 = 16 +1x 4 7 = 30 -3x 1 1 = ? = 1 1 = -12
It is clearly 8-digit based countung system, so... 3 + 5 = 16 (8 + 6 = 14); 8 -> 14 4 + 7 = 30 (3*8 = 32); 11 -> 32 Just by adding 3 to the left side the got a rise of 18 on the right. So, it correlares to a +1 -> +6 1 + 1 = 14 - 6*6 = -36 + 14 = -22 in 10-digit system, but we have 8-digit system, so it makes the final answer: 1 + 1 = -26 Have a nice day
Solving it as the mathematically equation he gave us (tho if it was a logic test, it shouldn't have just been a math equation), I actually did it a bit different. Let's assume that the number we're looking for is x: So we have 3a+5b+c=16 4a+7b+c=30 a+b+c=x Subtracting the 1st from the second, we get: a+2b=14 => a=14-2b Now, if we subtract the original 3rd equation (a+b+c=n), from the 1st, we get: 2a+4b=16-x Then we can substitute in the a=14-2b: 2(14-2b)+4b=16-x => 28-4b+4b=16-x => 28=16-x => x=-12
A much easier solution We've to find a+b+c, therefore when i wrote the equations as 3a+5b+c=(a+b+c)+2a+4b=16 and 4a+7b+c=(a+b+c)+3a+6b=30 i noticed we can convert these into two variable equations by taking a+b+c=x and a+2b=y So, x+2y=16 and x+3y=30 by solving we get x=-12 and x=a+b+c=-12
Nothing in the question to require that the function is linear in x and y The formula (x+1)*(y-1) is.mòre intuitive And a formula of that kind has only two unknowns (x+a)*(y+b) which is appropriate for two simultaneous equations.
I thought in this way: - 3+5 = 16 = 3*5+1 4+7 = 30 = 4*7+2 So, 1+1 = 1*1+(-1) = 0, as we're adding 2 and 1 respectively for the 1st terms 4 and 3, so if we assume the sequence, for the terms 4,3,2,1,..., we can add 2,1,0,-1 respectively.
Sir plz solve a question- X-Y=1 X^Y+Y^X=17 Find X and Y. No one knows the actual process rather they are just assuming values.Since there is a small no. we are able to assume values but for a big no. it's not our cup of tea to assume values.
I got the same answer by approaching the problem as a system of equations with two variables ! 3a + 5b = 16 4a + 7b = 30 => a = -38 => b = 26 => 1(-38) + 1(26) = -12
That's brilliant. c is irrelevant because it is the constant being added to ax+by, so you can assign it any number you want and it won't change the final result of a+b+c.
Yes, easily, though like other puzzles of this sort there are probably multiple legitimate answers. In this case, look at the addends as A and B, from left to right. Then understand that the addends are factors, because the plus sign means "times." Now for each A, subtract 1, and for each B, add 3. So each equation is satisfied by (A-1)(B+3). The final equation 1+1, therefore, is the equivalent of 0X4. One solution is therefore zero.
We have 2 equation on our hands therefore we must have 2 unknowns. So we must eliminate the c. Eliminate it then you'll find a+2b is 14. Multiply by 4 and you'll see 4a+8b is just one more b away from second equation. Work on that you'll find b. Rest is history. Did in my mind.
I have a simpler solution. Multiply first equation by 3, and second by 2 3* (3a+5b+c=16) -> 9a+15b+3c=48 2* (4a+7b+c=30) -> 8a+14b+2c=60 subtract. a+b+c=-12
The function has been stated as ax + by + c Accordingly, function of 3 and 5 = 3a + 5b + c = 16........ Eq i Function of 4 and 7 = 4a+ 7b + c = 30..........eq ii Subtract eq i from eq ii Then a + 2b = 14 Function of 1 and 1 = a + b + c 3a + 5b + c = 16 2a + 4b + a+b+c = 16 2(a + 2b) + a+b+c = 16 2*14 + a+ b +c = 16 Finally a+b+c = 16-28 = -12
For the thumbnail, there is no assumption for the form of the equation. Putting aside that they used "+" (which makes their statements incorrect for the standard definition of addition on integers), we might assume they are doing some "simple" combination of operations for the less mathematically inclined to follow. I good candidate for their operation is that you add 1 to the first input, subtract 1 from the second input, and then multiply those results together. In other words a "+" b = (a+1)(b-1). In this case, the answer would be 0. But in reality, this problem (like many so-called logic puzzles) is ill-defined and the answer could be anything.
markgriz The thumbnail (in other words, the logic puzzle expressed in a form that looks like a viral math problem) is ill-defined. This is the same as the initial way Presh presented the problem. Yes, he did then express it in the proper notation and with the restriction that the output is in the form ax + by + c (I did watch the video), so at that point we had a well-defined problem (and I understand this well-defined version is the one for which Presh gave a specific citation and asked us to pause the video and try to solve). We don't disagree on that, and I'm not sure why you'd think I would disagree on that. It seems that our disagreement is whether or not it's relevant to this video to comment on the initial presentation of the problem in the thumbnail. I think it is relevant. In other words, since Presh said "logic and intelligence tests like this one often spread across social media" while the ill-defined version was on the screen, my comment is relevant because it explains why the "social media version" of the problem would be ill-defined.
3 + 5 = 16 ( false)
4 + 7 = 30 ( false)
1 + 1 = 2 ( true )
You would be an excellent computer programmer. Boolean logic.
@@SkydivingSquid haha thx q
Lmao
No, 1=2
Explanation.
Let’s say a=b
Add a to both sides
2a=ab
Remove b
(a+b)(a-b)=b(a-b)
Cancel out (a-b)
A+b=b
But a=b so 2b=b
Divide by b
2=1
Best answer
I'm sorry but this is not a logic test. by labeling it as a logical test, you mislead people into solving the problem outside the conventional mathematical paradigm and into finding some different correlation between the numbers which are not related to direct, obvious computation.
this problem should have been labeled as: _solve the following mathematical equation_ .
Touché.
Ok
De acuerdo contigo. Agree with you.
The question was: Can you solve this logic puzzle? 2 things: it’s considered logic and a puzzle! Two things that are not necessarily genius. Anyone should be able to use basic logic or any other unconventional method to solve it.
You can in fact use a certain amount of logic here. We are told that x ⊕ y = ax + by + c, which is linear. Also notice that in all examples, x and y have a linear relationship: y = 2x−1.
As x increases/decreases by 1, y increases/decreases by 2, so x ⊕ y should increase/decrease by a+2b which is constant. Since the difference between 4 ⊕ 7 and 3 ⊕ 5 is 14, than a+2b = 14, and we get the following pattern:
4 ⊕ 7 = 30
3 ⊕ 5 = 16
2 ⊕ 3 = 2
1 ⊕ 1 = −12
am i the only one who got 0?
(3+1)*(5-1)=16
(4+1)*(7-1)=30
(1+1)*(1-1)=0
I got that
i got the same answer
yep
and me
I read the comments and ppl found 4 ways to get to 0
I thought it would be 4 based on a pattern I saw: 3x5+1; 4x7+2; 1x1+3. I know so little.
Joel Wetzel Honestly thats what I also thought
Same me too
Even me
Lol...what did u do with the function then😂😂
That's rhe solution that glances at first in the solver's mind.
3+5 = 16 I interpret as "3 x 5 +1"
4+7 = 30 I interpret as "4 x 7 +2"
Therefore 1+1 is "1x1+3=4" :)
This answer is also logic for me.
3*5=15,1 get out from 15 and add then =15+1=16
4*7=28,2get out from 28 and add=28+2=30
1*1=01,get 0 out from 01 and add=1+0=1
@@lucvanhove9639 It should not.Don't you think if intstead of 1+1,there will 2+3 ,then again we have to subtract 3.Which doesn't make sense.
it wasn't supposed to b tHis way !: just don't use series concept :: but 3+5=16 or (3+1) × (5-1)=16
4+7=30OR (4+1) ×(7-1)=30 similarly
(1+1) ×(1-1)=0
I did it with a slightly different rule : if both terms are odd, then add 1, otherwise add 2. Oddly, applying that rule gives "1+1 = 2" !!!
3a + 5b + c = 16
4a + 7b + c = 30
We want to know what a + b + c equals
9a + 15b + 3c = 48
8a + 14b + 2c = 60
a + b + c = -12
Forgive my ignorance, but how do you know what to multiply the original equations by? In this case you choose 3 and 2, but why those numbers?
Is it just any random numbers as long as you keep the equations equal?
That's what I got too. Zlatan knows MATH too? lol
its simply to get a + b + c
You can also find out you think you i
Same answer..👍👍👍
answer is 0
a+b = (a+1)(b-1)
my answer too
Even mine....
Haha!!
Me too
Same here
same
(3+1)*(5-1)=16
(4+1)*(7-1)=30
(1+1)*(1-1)=0 That's how i thought of it and it ain't wrong.
Same dude 🤣
It is wrong bud. You completely ignored the ax+by+c part of the problem.
@@mega1chiken6dancr9 I solved it before clicking on the video. Just saw the thumbnail and took a shot at it .
@@atharvkapila3336 well you jumped to your own conclusions before completely comprehending the problem. You are wrong
2 easy correct methods
Solving/realizing that it is this augmented matrix
3 4 | 1
5 7 | 1
16 30 | ?
2: realizing the pattern
3 5 = 16
+1x
4 7 = 30
-3x
1 1 = ?
=
1 1 = -12
Thumbnail is a bit misleading but overall good video.
Thumbnail is exactly what this puzzle looks like on social media
I wonder how many would watch the video if they knew what the problem actually was.
@Rayan same lol
Agree
Yeah
I've also found a simple solution:
(3+1) x (5-1) = 16
(4+1) x (7-1) = 30
So...
(1+1)x(1-1) = 0
Of course we can create any logic to associate the number... but I liked this one
The question included a rule to construct the operation. This doesn't follow it.
that's what I did
Also
X*Y+(Y-X-1)=z
3x5+(5-3-1)=16
4x7+(7-4-1)=30
1x1+(1-1-1)=0
I got the same
Answer is -12 not ZERO.
The way I solved it was I looked at it as a simple function. Before 3+5, you'd have 2+3, then 1+1. And subtract 14 as it goes down. And that still gives me -12.
Yes that what I did, its simpler
But you can't be sure that is the pattern unless they showed you atleast one more equation
If you write out your approach as:
4 + 7 = 30
3 + 5 = 16
2 + 3 = 2
1 + 1 = -12
the pattern is obvious, and also linear, so must correspond to PT''s answer, which assumed a linear solution. Just much easier.
This is also what I did. This is much simpler!
Totally how I got it in my head before playing the rest of the video. To do more formally, Eq2 - 2 * (Eq1 - Eq2) gets you there, or simplifying, -Eq2 - 2Eq3 => a + b + c = -12.
The question in the thumbnail was way more open-ended. For example floor(mean(x,y)^2) satisfies the first two equations, and so 1+1=1 would be the third.
Yeah thats what i thought before watching...
@@pedroafonso8384 he does that a lot where the thumbnail seems different/easier than the actual question. In his defense some questions are too long to fit a thumbnail but this one wasn't imho.
I must know a different version of floor and mean functions... Mean(3,5) should be (3+5)/2 = 4, and floor(x) should go to some rounded value, usually nearest whole number less than or equal to the input, meaning floor(mean(3,5)) would be 4, not 16... What definitions are you using such that floor(mean(3,5)) = 16?
@@Vertraic I totally forgot to type the squared part, thanks for double checking. Ijust edited to add that. In your version of the mean() function for whatever reason you decided to do integer division by 2 which also is a mistake.
@@Gideon_Judges6 is integer division a mathematical concept or just a computer concept? cause i don't remember them teaching me (5+3)/2 was integer division in grade school haha
3×5=15+1=16
4×7=28+2=30
1×1=1+3=4 that's my answer
This is going top comment lol
Lol you are everywhere
This guy is everywhere
Bruh u here too
You came up with the came thought as mine.
3+5=16,logic (3*5)+(5-3)-1,
4+7=30,logic(4*7)+(7-4)-1,
So logic is (a*b)+(b-a)-1,
So (1*1)+(1-1)-1=0
This can also be used
Neat that there was no need to solve a, b, and c themselves.
Pretty sure there is probably infinite answers for a b and c
There is infinate solutions, but I assumed the solution was a whole number so I got a result: a=2, b=6, c=-20 ... and it was correct (this is one of infinate solutions, but they all follow the same logic so if you get one of them u have solved the problem)
I tried it with b=10, got a=-6 and c=-16, same result of -12.
goldfndr the a, b, and c values need to work for x=3 y=5 and result=16 though. Otherwise it would work with literally any set of 3 numbers that adds to -12.
TRiG (Ireland). Well, I got using the substraction method:
a = -58
b = 36
c = 10
Greetings from Colombia!
My ans is 4 and this how I got it :
3 * 5 + 1=16
4 * 7 + 2 = 30
1 * 1 + 3 = 4
That's what I was thinking too.
Same
same
But there is no ordering here to use some logic of that kind
Same
My solution
(3*5)+1=16
(4*7)+2=30
(1*1)+3 =4
I was thinking that x and y were getting closer together in value and multiplied.
If x=/=y, subtract 1 from the larger number and add 1 to the bigger number. Then multiply.
3 1×1=1
With a simpler rule set you would have gotten the last row to be
1+1 × 1-1 = 2×0 = 0
Can you guess the next answer then:
(?*?)+4=?
@@Goejii yes
Thought the same way lol
My instant answer. And I have a Mensa diploma.
Another way to solve it as follows
A. 3x + 5y + c = 16
B. 4x + 7y + c = 30
Now substruct A from B will get
C. X + 2y = 14
Now multiply A by 4, and multiply B by 3, will get
D. 12x + 20y + 4c = 64
E. 12x + 21y + 3c = 90
Now substruct D from E will get
F. y - c = 26
Now substruct F. from C. , will get
x + 2y - ( y - c ) = 14 - 26
Or
x + y + c = 12
This is all
3 + 5 = 16 --> 3x5 [15] + 1 [first digit of 15] = 16
4 + 7 = 30 --> 4x7 [28] + 2 [first digit of 28] = 30
1 + 1 = 2
Interesting. I did +1 first answer, +2 second so +3 on the third, therefore "1+1" = 4
Alternative method: (1) 3a+5b+c=16 (2) 4a+7b+c=30 (3) a+b+c = x. (2)-(1) gives a+2b = 14 so 3a+6b = 42, (2)-(3) gives 3a+6b = 30-x. 30-x = 42 so x = -12.
the answer is actually
3 + 5 = 16 ❌
4 + 7 = 30 ❌
1 + 1 = 2 ✅
I just figured out that a+2b=14 and then figured that 3a+5b+c-2a-4b=a+b+c, 3a+5b+c-2a-4b=(3a+5b+c)-2(a+2b)=16-2*14=-12.
That's how I did it
Yay! This is the first MindYourDecisions problem I solved correctly
It's just a basic exercise in linear algebra. With the first two equations, I created an augmented matrix and did row reductions. Obviously, c will be a free variable; that means that the solutions to a and b will be written in terms of c. Set the solutions to a and b equal to each other and solve for c. Put the value of c back into one of the equations and you will get the value of both a and b because we just found the point where a = b. Now we have a, b, and c so just add them up since the coefficients equal 1
I've seen a lot of tests in which "c" is not constant throughout the expressions but it lineary increases according to the position of the expression.
So in this case you would have
a1 * b1 + 1
a2 * b2 + 2
a3 * b3 + 3
and so on.
When such tests have a multiplicity of solutions they are either malformed or they just need more example cases to constrain the possible answer.
Questions like this always have an infinite number of solutions.
The answer to this problem depends on how you define ⊕. You do indeed get -12 with your linear algebraic definition, but other solutions are valid as well. In addition, I prefer a more systematic approach, however, such as doing matrix reduction on the 3 equations. You end up getting b - c = 10 - 4k/3 and b - c = 8 - 3k/2, where k is a constant solution for 1 ⊕ 1. Therefore, the only way for the system of equations to have a solution 10 - 4k/3 must equal 8 - 3k/2. After solving for k, k= -12.
If the relationship between x and y is not given, then it can be any relationship you want. There was no relationship given in the thumbnail or in the "logic and intelligence tests that spread across social media" until _Presh stated that the puzzle was _*_based on_*_ a well known relationship, and then went on to solve _*_that_*_ relationship._
Given the original puzzle _as presented_ (on social media and in the thumbnail), the solution can be any value you like - you will be able to find a polynomial function of x and y which gives the results for the two given results and gives the value you want for the third (I'm not saying it will be easy[1], just that it is possible to find such a function to justify the result).
For example, if:
f(x,y)=11x^3 - 79x^2 + 80y + 30
then
f(4,7) = 30
f(3,5) = 16
and
f(1,1) = *42*
And that's the answer: *FORTY TWO*
[1] actually as there are infinitely many such polynomials it is fairly easy to find one of them.
exactly.
1+1=2. Just because the first two equations are wrong, doesn't mean you should also answer the third one incorrectly. Thats how I read it.
You are pretty dom, that "+" is an operator, can mean anything as defined.
I challenge that argument and say it's 4.
3 + 5 = 16
......(3 times 5 is 15... it's the 1st in the sequence so add 1....16)
4 + 7 = 30
.....(4 times 7 is 28....it's the 2nd in the sequence so add 2....30)
1 + 1 = 4
.....(1 times 1 is 1....it's the 3rd in the sequence so add 3.....4)
The only way you can get 12 is if you are DEFINITELY given the equation (ax + bx + c)... otherwise you could never logically make that assumption to be true.. that's not how code breaking works... and I am sure there are many other methods people could come up with to solve for other variables. You'd need more than 2 examples with "answers" to narrow it down....
I also solved this way
i also thought this
I was this way...
(a,b) = a×b + [a/2]
where [ ] stands for G.I.F.
So, (3,5) = 3×5 + [3/2] = 15 + 1 = 16
And, (4,7) = 4×7 + [4/2] = 28 + 2 = 30
Therefore, (1,1) = 1×1 + [1/2] = 1 + 0 = 1
3/2 isn't 1 what are you talking about
@@Renitky yes it's 1. But wrote [3/2] = 1
[ ] denotes the greatest integer function (In laymen's terms it means the integral value of "3/2" or "1.5" which is "1").
I graphed the two equations as:
3x+5y=16
4x+7y=30
These two lines intersect at (-38, 26), which led me to answering -12.
I feel like I would get that “You used the wrong equation, but got the right answer” written on my test.
Missed the Gougu Theorem here 🥺🥺
After subtracting (1) from (2) to get a+2b=14 it is simpler to subtract 3 x (1) from 4 x (2) to get b-c=26. Subtracting the second result from the first result yields a+b+c=-12.
Hey Presh why cant we do it as follows
3×5 +1=16
4×7 +(1+1)=30
Then,
1×1 +(1+1+1)=4
Because it's not the actual numbers 3 and 5 or 4 and 7, rather these are variables. You adding 1 to the first equation and 2 to the second and getting a correct answer is nothing more than a fluke
What are you trying to do there? It looks completely unrelated to the problem...
There are another options, gives answers such as 0 or -1. But the form of the question is given, so the answer is -12.
The rule was given that the operation adds ax+by+c. That wasn't a tool for solving the problem, it was a constraint that is part of the question. Your method doesn't follow the rule.
That's the reason I dislike problems like this - you can find any answer if you look long enough
I came up with "0" from seeing the thumbnail with an operation of (x * y) + (|x - y| - 1)
A solution is only possible, in this form, because the third equation is a linear combination of the first two. Other solutions, such as the ones that come up with zero are also valid, particularly if you have been baited here by the original thumbnail!
I get the feeling that he overlooked the method that results in zero which I thought would be the most obvious (simple math).
0. An answer, or more precizely , one of the possible answers, is zero. Two upper lines satisfy the following expression (A+1)*(B-1) = C since (3+1)(5-1) = 16 and (4+1)(7-1)= 30 so (1+1)(1-1) = 0
I did something like this
3+5=(3+1)*(5-1)=16
4+7=(4+1)*(7-1)=30
1+1=(1+1)*(1-1)=0
What's the problem in this solution
Correct answer is 0.
Let x be the first number and y the second number.
The formula to find the correct answer would then be xy+x-2.
Note that this formula satisfies both the given equations.
So the answer is 1*1+1-2=0
Also xy+(y-x)-1
For this type of riddles you need more than 2 examples . There could be different reasons.
3+5 = 16 => (3+1) x (5-1)= 4 x 4 = 16 ; 4 + 7 = 30 => (4+1) x (7-1) => 5 x 6 = 30 ; Hence 1 + 1 => (1+1) x (1-1) => 2 x 0 = 0
I thought the answer was zero😅
Alot of people in the comments got zero, assuming it was (a+1)(b-1) which is a formula that would also satisfy the other two equations
1+1=? (-1)
2+3=y. (0)
3+5= 16. (1)
4+7=30 (2).......see my solution you will understand why had I typed (-1), 0, 1 and 2....Can you see the pattern?
3×5+1=16
4×7+2=30
Therefore, following the same pattern
1×1+(-1)=0
when I first looked at the thumbnail I thought it was 0
adding 1 to the first number, subtracting one from the second and then multiplying them
3@5 -> 4*4=16
4@7 -> 5*6=30
1@1 -> 2*0=0
Boy... I was so wrong...
You made this WAY too complicated. Once you have a+2b=14, just double that to get 2a+4b=28. Then subtract that from your first equation:
3a-2a+5b-4b+c=16-28
a+b+c=-12
This was is easy enough I could do it in my head in about a minute. Your waynis much harder.
I approached it thusly (I'm using "X" for the binary operator here):
3 X 5 = 3a + 5b + c = 1 X 1 + 2a + 4b = 16 (since 1 X 1 = a + b + c)
4 X 7 = 4a + 7b + c = 1 X 1 + 3a + 6b = 30
Multiply top equation by 3 and bottom by 2 to balance a & b, then subtract, leaving:
1 x 1 = -12
Does '+' mean something different than addition? Why didn't they use the operator you showed if they meant it was some function other than addition?
It's called binary operations
They are forcing you to make the arguments true in order to find the final answer of X. So, “+” might need to be a different function. Since the arguments don’t equate even with that, there must be an invisible variable of “c” in play.
My process?
3 * 5 + c1 = 16 = 15 + 1, c1 = 1
4 * 7 + c2 = 30 = 28 + 2, c2 = 2
So it follows that;
1 * 1 + c3 = X = 1 + c3,
Since the “c” value increases by 1, c3 must be equal to 3. So;
1 * 1 + c3 = X = 1 + 3 = 4
Thus;
X = 4
That's annoying really
@@hanifkhairi4926 Maths in a nutshell
Welcome to the world of abstract algebra!
We might make the assumption that the + operator forms a group over the set on integers. In this case, we must verify the following properties:
Closure:
a+b always results in another integer.
Associativity:
a+(b+c) = (a+b)+c
Existance of a "zero" element:
For any a, there exists zero such that a+zero = zero+a = a
Invertability:
For any a, there exists b such a+b = b+a = zero
Ordinary arithmetic has two well known groups. Addition forms a group over the integers in the way we naturally expect. Multiplication forms a group over the rationals, since we require fractions for the inverse, and we need to note that the "zero" identity is actually the number 1.
Hi! I solved it more simply.
Subtracting the second equation to the first one:
4a + 7b + c = 30
- 3a - 5b - c = - 16 ---> a + 2b = 14
Then substituting it in the first equation:
a + b + c + 2a + 4b = 16
a + b + c + 2(a + 2b) = 16
a + b + c + 2*14 = 16
a + b + c = -12
3 X 5 + 1 = 16
4 X 7 + 2 = 30
1 X 1 + 3 = 4
So 1 + 1 = 4 , maybe I’m the only one .
And 4+6=?
I initially thought this when I saw the thumbnail but after starting the video I realized it wasn’t that simple ... they never are on this channel.
I did the same
That seems fair if this was just pattern recognition but it is actually pure Math.
More like, 3 x 5 + {(5 - 3) - 1} = 16
4 x 7 + {(7 - 4) - 1} = 30
So, 1 x 1 + {(1 - 1) - 1} = 0
But i think i am also the only one!
Another way is to substitute 1 equation from the second and you will get:
a + 2*b = 14
Then substitute third equation from the first, you will get (z is answer):
2*a + 4*b = 16 - z
Base on the first equation we know that 2*a+4*b=2 * (a + 2*b) = 2 * 14 = 28.
So:
28 = 16 - z - > z = -12
How about this?
(3-1)*(5+3)=16
(4-1)*(7+3)=30
(1-1)*(1+3)=0
Did you even watch the other comments in this video. I know this is not the solution of actual problem. But there is a lot of people that are explaining their own answers they thought by looking thumbnail. I thought this answer when I looked thumbnail, so I wanted to introduce my answer like others do.
@@SoloNit Actually it is not relevant to the actual problem. I did not write this comment to explain the solution of the actual problem, but only to share that there is another way to make 16 and 30 if there is no restriction from the actual problem.
From the first equation, when x=3 and y=5, we have:
3a + 5b + c = 16
From the second equation, when x=4 and y=7, we have:
4a + 7b + c = 30
We can use these two equations to solve for a, b, and c. One way to do this is to eliminate the constant c by subtracting the first equation from the second equation:
4a + 7b + c - (3a + 5b + c) = 30 - 16
Simplifying this equation gives:
a + 2b = 7
We now have two equations:
3a + 5b + c = 16
a + 2b = 7
We can use the second equation to solve for a in terms of b:
a = 7 - 2b
Substituting this into the first equation gives:
3(7 - 2b) + 5b + c = 16
Simplifying and rearranging terms yields:
-6b + c = -5
We can now solve for c in terms of b:
c = -5 + 6b
Substituting this into the equation a + 2b = 7 gives:
(7 - 2b) + 2b = 7
Solving for b gives:
b = 2
Substituting this value of b into the equation a + 2b = 7 gives:
a + 4 = 7
Solving for a gives:
a = 3
Finally, we can substitute the values of a, b, and c into the original equation ax + by + c:
3(1) + 2(1) + (-5) = 0
Therefore, when x=1 and y=1, the value of ax + by + c is 0.
3*5+1=16
4*7+2=30
1*1+3=04
Can't it be this simple🤷🏼♂️
This is absolutely the same method I used, and one far more logical for "code breakers"; but as you will see, other great methods were used to find different answers. I for one, think that using "ax + bx + c" is a terrible and arguably illogical assumption to make. It depends on if it was provided or not.
3+5 => 3*5+(1) = 16(from 3*5 15 i keep the num 1)
4+7 => 4*7+(2) = 30(from 4*7 28 9 i keep the num 2)
1+1 => 1*1+(0) = 1 (from 1*1 01 i keep the num 0)
the pseudo-formula is :
a+b =c =>> a*b = c (from ab i keep the first digit of the product ab ,let it be d)
so "a+b" => c = a*b +d
I got -12, but find how you did it interesting. I showed that c = 0 earlier (by rearranging one equation and substituting it into another) and solved the simultaneous equations I was left with. I guess your method is better as it involves less steps.
Mine has even fewer steps : solver a+2b = 14 then multiply by 3 to get 3a +6b =42 then substrate that from 4a+7b+c =30 and get a+b+c =-12
@@gastplayz347 i just did a+2b=14 and did trial and error and got 0x+7y-19 the first try (correct)
From the thumbnail, thought the rule was:
a + b = (a+1)(b-1), giving
1 + 1 = 2(0) = 0
Obviously then I realised the video had a question itself nothing to do with this
A good question on finding a three variable equation using only two given equations.
# A very particular solution. 👍👍👍👌👌👌
A solution is only possible, in this form, because the third equation is a linear combination of the first two.
@@gordoncharles741 I completely agree with you 👍👍👍
Multiply first eq by 3 and 2nd eq by 2 and subtract 2nd eq from first.
9a+15b+3c = 48
-. 8a+14b+2c =60
_-------------------------
a+b+c = -12
Quicker than Presh and no Gougu theorem needed
why must x # y = ax + by + c in the first place? is that even stated on the question?
Because that's what stated in the problem @0:14. "Suppose we have a binary operation...." and it goes on to clearly state how that binary operation is defined. How is this confusing to so many people?
The problem never said to invent your own binary operation.
Assuming that linearity holds, just multiply the first equation by 3, the second equation by 2 and subtract the second from the first, i.e. 3*(3+5)=3*16=48 and 2*(4+7)=2*30=60, then (9+15)-(8+14)=48-60, so 1+1=-12.
(5-3)×8=16
(7-4)×10=30
(1-1)×12=0
I did it this way: first you define, as per 0:40,
3a+5b+c=16
4a+7b+c=30
a+b+c=X (we're looking for X here)
Substract the first equation from the second and you get a+2b=14
Multiply that by 2 and you get 2a+4b=28
Substract that from the first equation and you get a+b+c=-12
a+b+c=X, so X=-12
This is super easy! It's just the two numbers and the first number in the row below!
3+5+4 = 12
and 4+7+1 = 12
The pattern reveals itself!
just joking
Holy sht 😂😂 I thought that was real 🤣
Answer can also be (x+1)*(y-1). That would give you 0. Why should some linear function be assumed?
Your channel is awesome bro.
I thought this was gonna be one of those viral problems where you could come up with all kinds of formulas which gives all kinds of different results for 1@1, but then the rules were more clearly explained and it turned into an algebra problem. Substitute x and y to make the following equations: 3a+5b+c=16, 4a+7b+c=30, a+b+c=? If we subtract the first 2 equations, we can solve that a=14-2b. Substituting back in to one of the equations, we can solve that c=b-26. Now if we plug those into the 3rd equation we get (14-2b)+b+(b-26) = ? The b's cancel out giving us 14-26=-12.
1+1=fish
thats one way of looking at it, but from my logic, it says 0, just apply this a+b = (a+1)(b-1)
3 + 5 = (3 +1)(5 - 1) = 16 and similarly for others
That guy: Now all we have to do... now we just... we easily do... bla bla bla JUST EASY VERY NORMAL
Me: uhm
What
You can just subtract 2*(4a+7b+c) from 3*(3a+5b+c) , which is equal to a+b+c; on the other side it's 3*18-2*30, which is equal to -12 and then you already have your solution
I thought its 4 😆
me too
Me too
Yup * edit* after watching i feel broken now lol..
Me tooooooo!!! T~T
Ok, glad I wasn't the only one
sir 0 also can be the answer to this problem ,my solution:- 3*5+((5-3)-1)=16,4*7+((7-4)-1)=30,similarly 1*1+((1-1)-1)=0
I THOUGHT THE ANSWER IS SIMPLY "2"
Yes it is. And the answers for the first two equations are 8 and 11. They were calculated wrong by a math professor.
The problem with this is, given the original question, you can find multiple patterns that give a valid answer. your proposed solution is just one assumption of many. therefor, the question itself is ambiguous (you see the same problem in some iq tests by the way).
1+1 is still 2 no matter what the first two statements say.
This method is hard to understand
you can make it so much easier by applying :
3x + 5y = 16
4x + 7y = 30
x + y = ?
searching X and Y with elimination method ( I find it easy ) with :
12 x + 20 y = 64
12 x + 21 y = 90
and y = 26
substitute that to
3x + 5y = 16
x = -144/3
x = -38
then add those two
1x + 1y = (-38) + 26
x + y = -12
there, I know it's longer but for me it's easier to understand.
Nobody:
Me: ❶
Since we get a-2b=14(equation 3) by subtracting the 1st equation from the 2nd equation, we can multiply the 3rd equation by 2 to get 2a-4b=28(equation 4). Then substract 2a-4b=28(equation 4) from 3a+5b+c=16( equation 1) to get a+b+c=-12
(Another Method)
3 * 5 + 1 = 16
4 * 7 + 2 = 30
1 * 1 + 3 = 4
1+1=? (-1)
2+3=y. (0)
3+5= 16. (1)
4+7=30 (2).......see my solution you will understand why had I typed (-1), 0, 1 and 2....Can you see the pattern?
3×5+1=16
4×7+2=30
Therefore, following the same pattern
1×1+(-1)=0
Did anyone point out, the problem is only soluble because the left-hand sides 3a+5b+c, 4a+7b+c and a+b+c are linearly dependent. This is because the determinant of the 3x3 coefficient matrix is zero. Given that, we know there will be a nulling vector (A,B,1) such that A(3a+5b+c)+B(4a+7b+c)+(a+b+c)=0 regardless of a, b and c. Thus 3A+4B+1=0, 5A+7B+1=0, A+B+1=0. Solve any two of these for A=-3, B=2. Then 16A+30B+x=0, x=48-60=-12.
this's way better
4a + 7b + c - (3a + 5b +c ) = a + 2b = 30 - 16 = 14
=>2a + 4b = 28
=> 3a + 5b + c - ( 2a + 4b ) =16 - 28 = -12
Odd, I tried taking an intuitive approach to this
5+3=8*2=16
4+7=11*2=22+8=30
So therefore using that same logic of multiplying the result by 2 and adding the previous sum of the last pair
1+1=2*2=4+11=15
First of all I am tempted to think of addition in other bases (thus 3 + 5 = 12 in base 6, but no base could ever allow 4 + 7 to equal three times the base because 11 is not a multiple of 3.In base-8, the smallest base that can allow "7" as a digit, 4 + 7 = 15.
I think at least three clues are needed to get a single function.
One way to conceptualize this would be to replace the addition sign with multiplication, and determine what missing quantity would add up to the number in question; then decrement by one each time. In that case:
4x7 [+2] = 30
3x5 [+1] =16
2x3 [+0] = 6
1x1 [-1] = 0
Another would be to add the numbers, and find out what addend is needed to produce the final result, but subtract 11, increasing by a factor of one each successive time:
4 + 7 [+19] = 30
3 + 5 [+19-11] = 16
2 + 3 [+19-22] = 2
1 + 1 [+19-33]= -12
Both of these make perfectly reasonable - but different - sequences.
My point is that there are many (in fact, infinite) series that result in the same sequence of numbers - for any finite portion of a "series." There is no single answer for a problem like this.
If you doubt that, check out the on-line encyclopedia of integer sequences: oeis.org/
I arrived at 0 using your first solution too.
EASIER SOLUTION:
Just look at row operation trends, 3->4 has is an addition of 1, 4->1 is a subtraction of 3. Then on column 2, 5->7 is the addition of 2, 7->1 is the subtraction of 6. Thus the difference between row 1 and 2 of a given column is 1x, where x is a number you can easily find, and rows 2->3 has a difference of -3x. On the right, it is 16->30 which makes x=14. Then from 2->3, it's 30-3(14) = y and that gives you negative 12. Right it out visually it is WAY easier to solve it like this.
3 5 = 16
+1x
4 7 = 30
-3x
1 1 = ?
=
1 1 = -12
It is clearly 8-digit based countung system, so...
3 + 5 = 16 (8 + 6 = 14); 8 -> 14
4 + 7 = 30 (3*8 = 32); 11 -> 32
Just by adding 3 to the left side the got a rise of 18 on the right.
So, it correlares to a +1 -> +6
1 + 1 = 14 - 6*6 = -36 + 14 = -22 in 10-digit system, but we have 8-digit system, so it makes the final answer:
1 + 1 = -26
Have a nice day
Solving it as the mathematically equation he gave us (tho if it was a logic test, it shouldn't have just been a math equation), I actually did it a bit different.
Let's assume that the number we're looking for is x:
So we have
3a+5b+c=16
4a+7b+c=30
a+b+c=x
Subtracting the 1st from the second, we get:
a+2b=14 => a=14-2b
Now, if we subtract the original 3rd equation (a+b+c=n), from the 1st, we get:
2a+4b=16-x
Then we can substitute in the a=14-2b:
2(14-2b)+4b=16-x =>
28-4b+4b=16-x =>
28=16-x =>
x=-12
A much easier solution
We've to find a+b+c, therefore when i wrote the equations as
3a+5b+c=(a+b+c)+2a+4b=16 and
4a+7b+c=(a+b+c)+3a+6b=30 i noticed we can convert these into two variable equations by taking a+b+c=x and a+2b=y
So, x+2y=16 and x+3y=30 by solving we get x=-12 and x=a+b+c=-12
Nothing in the question to require that the function is linear in x and y
The formula (x+1)*(y-1) is.mòre intuitive
And a formula of that kind has only two unknowns (x+a)*(y+b) which is appropriate for two simultaneous equations.
I thought in this way: -
3+5 = 16 = 3*5+1
4+7 = 30 = 4*7+2
So, 1+1 = 1*1+(-1) = 0, as we're adding 2 and 1 respectively for the 1st terms 4 and 3, so if we assume the sequence, for the terms 4,3,2,1,..., we can add 2,1,0,-1 respectively.
Sir plz solve a question-
X-Y=1
X^Y+Y^X=17
Find X and Y.
No one knows the actual process rather they are just assuming values.Since there is a small no. we are able to assume values but for a big no. it's not our cup of tea to assume values.
I got the same answer by approaching the problem as a system of equations with two variables !
3a + 5b = 16
4a + 7b = 30
=> a = -38
=> b = 26
=> 1(-38) + 1(26) = -12
That's brilliant. c is irrelevant because it is the constant being added to ax+by, so you can assign it any number you want and it won't change the final result of a+b+c.
@@chinareds54 I have seen some rather elegant solutions using c in the comments, admittedly! And I appreciate being exposed to the method in the video, with the x © y = ax + by + c, which I've never seen before
I got this by parameterizing the line.
Consider (3+t,5+2t,16+14t)
t=0 gives the first equation, t=1 gives the second, and t=-2 gives the third.
Yes, easily, though like other puzzles of this sort there are probably multiple legitimate answers. In this case, look at the addends as A and B, from left to right. Then understand that the addends are factors, because the plus sign means "times." Now for each A, subtract 1, and for each B, add 3. So each equation is satisfied by (A-1)(B+3). The final equation 1+1, therefore, is the equivalent of 0X4. One solution is therefore zero.
When u arrive at (a + 2b) = 14. Multiply this by 2 to get (2a + 4b = 28) and subtract this from (3a + 5b + c) = 16 to get (a + b + c = -12)
A system of two linear equations is easy to solve:
3a+5b=16
4a+7b=30
And there is absolutely no need to consider _c_ .
Is this weird?
3 * 5 + (3 - 2) = 16
4 * 7 + (4 - 2) = 30
1 * 1 + (1 - 2) = 0
We have 2 equation on our hands therefore we must have 2 unknowns. So we must eliminate the c. Eliminate it then you'll find a+2b is 14. Multiply by 4 and you'll see 4a+8b is just one more b away from second equation. Work on that you'll find b. Rest is history. Did in my mind.
I have a simpler solution.
Multiply first equation by 3, and second by 2
3* (3a+5b+c=16) -> 9a+15b+3c=48
2* (4a+7b+c=30) -> 8a+14b+2c=60
subtract.
a+b+c=-12
The function has been stated as ax + by + c
Accordingly, function of 3 and 5 = 3a + 5b + c = 16........ Eq i
Function of 4 and 7 = 4a+ 7b + c = 30..........eq ii
Subtract eq i from eq ii
Then a + 2b = 14
Function of 1 and 1 = a + b + c
3a + 5b + c = 16
2a + 4b + a+b+c = 16
2(a + 2b) + a+b+c = 16
2*14 + a+ b +c = 16
Finally a+b+c = 16-28 = -12
For the thumbnail, there is no assumption for the form of the equation. Putting aside that they used "+" (which makes their statements incorrect for the standard definition of addition on integers), we might assume they are doing some "simple" combination of operations for the less mathematically inclined to follow.
I good candidate for their operation is that you add 1 to the first input, subtract 1 from the second input, and then multiply those results together. In other words a "+" b = (a+1)(b-1). In this case, the answer would be 0.
But in reality, this problem (like many so-called logic puzzles) is ill-defined and the answer could be anything.
It isn't ill-defined. You need to watch the video, not look at the thumbnail
markgriz The thumbnail (in other words, the logic puzzle expressed in a form that looks like a viral math problem) is ill-defined. This is the same as the initial way Presh presented the problem.
Yes, he did then express it in the proper notation and with the restriction that the output is in the form ax + by + c (I did watch the video), so at that point we had a well-defined problem (and I understand this well-defined version is the one for which Presh gave a specific citation and asked us to pause the video and try to solve).
We don't disagree on that, and I'm not sure why you'd think I would disagree on that.
It seems that our disagreement is whether or not it's relevant to this video to comment on the initial presentation of the problem in the thumbnail.
I think it is relevant. In other words, since Presh said "logic and intelligence tests like this one often spread across social media" while the ill-defined version was on the screen, my comment is relevant because it explains why the "social media version" of the problem would be ill-defined.