16 main grid 1x1 squares 9 main grid 2x2 squares 4 main grid 3x3 squares 1 main grid 4x4 square 8 small grid 1x1 squares 2 small grid 2x2 squares For a total of 40 squares!
Taking your notes about squares a step further, I noticed something potentially interesting. The next logical number in the sequence is 25, or 5^2. ...that's how many "intersections" there are.
In these square puzzles they don't state that the squares that bisect the lines are at the midpoints. Without that, we can't know if the bisecting lines create 4 new squares.
Starting small .. and getting bigger There are 8 tiny squares (1/4 x 1/4) 8 there are 4 rows of 4 small squares (1 x 1) + another 2 18 there are 3 rows of 3 larger squares (2 x 2) 9 there 4 squares that are 3 x 3 4 and then there is a 4 x 4 square 1 TOTAL 40
Right! But, i would have said there is only 1 3×3 square, unless you want to count some of the rows and columns again and look at it from a different side. And i would have said there are 4 2×2 squares...for example, when you start from the upper left side why would you count the 2nd column again?
I have a rectangle and I would like to know how to calculate the dimensions for squares in multiples of 3. I need 3 wide, how many tall I need depends on the volume required to be covered in the rectangle. Hope you can help thankyou.
Squares of side length 1/2 = 8 + Squares of side length 1 = 18 + Squares of side length 2 = 9 + Squares of side length 3 = 4 + Squares of side length 4 = 1 Total = 40.
The answer is 40, if I’m correct we have to count carefully so take the 2 small squares in the middle away so we can walk through this clearly, we have 1 big square (4x4) and we can only make 1 of that. Next we have 3x3 you can make 4 squares with these 3x3. Now we have 2x2 you can make 9 squares with those 2x2. Now, we can count the 1x1 you can make 16 of. So we now add 1+4+9+16=30. Next, we can add those squares back from the middle that we took away. Now we can count that there are 2 big squares. Now the small squares, if there are 4 in each and there’s 2, that makes 8 So 30+2+8=40. Y’all welcome! 🤗
I'm going to referencing your video three moving squares in three moves for more of a clarification of what I mean. You have really small red squares on all the brown lines. Those red squares are the same size as white ones in this video. Thanks
Why wouldn't you count the other squares? Like the 1x2 and the 2x3 squares etc. aren't they also squares? I thought those also counted so I got to something like 86 before I stopped cause I couldn't bother
The problem statement is under specified. What counts as a square? Can it contain only white space? Can it contain other lines? We don't know until the "solution" is presented. Of course people get it wrong when there is more than one valid answer.
The argument why there are 2n-1 new 2x2 squares and so on isn't quite verbose... (Also technically the base case is missing.) But considering the comments most viewers care more about the number of squares. ;-)
I know an easier way. For a n x n square the solution to the number of squares is ((n)(n+1)(sum of two previous numbers))/6. Example: 4x4 square: ((4)(5)(9))/6 = 30. 2x2 square: (2x3x5)/6 = 5. It's easier to do than than square sums as multiplication cancels out.
Here's a riddle.... What is the probability of this channel finding a challenging riddle? Solution: Well there are a couple of methods to find the correct answer Method1: counting every riddle so we have 0challenging riddles and 73635 easy/bullshit riddles.... I might have miscounted that but it doesn't matter because 0/X is 0... So we can't expect any challenging riddles Method2: praying for better riddles.... We will get the result but this method takes a looooong time to work... Just like the method in this video.... It takes forever.... LITERALLY
by you *making* all the squares you can make you get to 40... but again... the true square is 1 (X), inside that one big Square your counting what forms it to be that value. so again. all the Squares you can see is 40 but it's not equivalent to X if you add them up... If you add up all the Squares (of the same size ignoring the little ones at the center you) there's 16 in total which is equivalent to (X) the big square. imagine this... X=to 16... "fractions" that make up for the hole piece (of square) if you divide 16 with 16 you get one which is equal to "the big square". soo again the answer can differentiate of how many "Exact" Squares there are... "but" the Big one is equal to the 16 smaller Squares. Key point: you can only get to 40 by "ignoring" the exact value of X, by adding all the different square shapes "you make" and adding them up in a way it's not equivalent to the exact value of X Square.
I've counted 40, and I must say that this is one of those easy tests for small children. I don't know why I even bother clicking these kind of videos. Maybe I just want to have false sense of being smart, no?
It seems like there are more squares that you missed if. you count the the optical illusion squares that happen inside the grid. There is a tiny Square at each line intersection except for the four corners of the largest square. Please disregard is this comment is annoying.
shit, I counted the rectangles as well, I got like 110 or something. I didn't know the term "square" was only "4-gons" with equal side lengthes. Now I feel like a complete dummie...
48 OR 44 OR 40 Edit:FORGOT THE 12 SQUARES OR 8 OR JUST 4 AND I ADD THIS IF n= 6.9282032303 the answer is 48 then if n= 6.3245553203 the answer is 40 and if n= 6.6332495807 the answer is 44
That is so bogus it is silly. It all revolves around how you define "a square." In my mind, a "square" has four equal length sides with 90 degree corners that contains *nothing else*. By *that* definition there are 16. Once again, semantics.
Per definition, a square has four equal length sides with 90 degree corners. The last part you said is mathematically not required for an object to form a square. This is not semantics, how you call it; a square is a well-defined object and therefore, the picture contains 40 of them.
If you have to remove squares to count , your changing the picture and creating a false narrative . The two squares you removed made the others obsolete and they are part of the picture . Perspective is everything . In all actuality there are 21 squares without an overlap . Once you add the overlap you can't just remove it ; It's part of the picture .
The correct answer should be 32, because the 8 1x1 squares in the inside columns are actually L shapes and not squares. It's all a matter of perspective. If you don't take the picture apart the answer is 32.
Who came here from The Mole
😂🙋♀️
Me 😂😂😂😂 I counted 35 😂😂😂
@@AyomisCorner I had to pause. I counted 40 on the screen like a toddler...not sure I'd have beaten the clock though.
MEEEE
Lmaoooo meee, because why was i counting 36
Glad you squared that all up for me.
Get out
lol
Leave this dimension for GOOD!!!!
Go off the grid!!! Wait.... SHIT!
Aren't those rectangles??!!!!! 3*3??!!
40 was my guess EDIT: I almost forgot the last one though, the biggest one :-D
You almost forgot the biggest one!? I forgot the "big middle" squares entirely and got 38 :(
+xisumavoid Why am I not surprised to see you on a video like this :D
Omg Xisuma ur awesome! Btw I got 39 only :(
+xisumavoid hiiii
Hi xisuma didn't expect to c u here
16 main grid 1x1 squares
9 main grid 2x2 squares
4 main grid 3x3 squares
1 main grid 4x4 square
8 small grid 1x1 squares
2 small grid 2x2 squares
For a total of 40 squares!
The total number of squares in any n × n array can be modelled by the formula
Total Squares = n(n+1)(2n+1)/6
But I'd have to add the irregular ones in the middle after, right?
Taking your notes about squares a step further, I noticed something potentially interesting. The next logical number in the sequence is 25, or 5^2. ...that's how many "intersections" there are.
In these square puzzles they don't state that the squares that bisect the lines are at the midpoints. Without that, we can't know if the bisecting lines create 4 new squares.
My favorite part of "Empire Strikes Back" was when the rebels wrapped the ropes around the legs of the Presh Talwalkars to knock them over.
zebra3stripes Civil War!! 🕸
Wrong video
Got the correct answer 40. Also enjoyed the inductive proof for general convention.
I am no good at math but I have good eyesight, insight and foresight and I get 40 ... definitely 40.
Not 39 nor 41 but 40 . TY
Another think I would like to point out, it may be obvious to some, is that this works with rectangular grids.
Most of the lines overlap making a new shape with more sides
That is what I thought
We're only looking for squares, though.
Rectangles or other polygons don't count.
1 big square, 4 large squares, 9 medium squares, 16+2 small squares and 8 tiny squares
40
Hey its basically like counting the perfect squares including the area of the whole square itself
Size of squares - Number of square
4x4 squares - 1
3x3 squares - 4
2x2 squares - 9
1x1 squares - 16
Big squares in Middle - 2
Small squares in Middle square - 8
I count a total of 35. All squares must have the same length on each side. That's the primary rule
+Tyler Kane it's 40 actually
Also called square pyramidal numbers. The formula is n*(n+1)*(2n+1)/6 for sidelength n.
Starting small .. and getting bigger
There are 8 tiny squares (1/4 x 1/4) 8
there are 4 rows of 4 small squares (1 x 1) + another 2 18
there are 3 rows of 3 larger squares (2 x 2) 9
there 4 squares that are 3 x 3 4
and then there is a 4 x 4 square 1
TOTAL 40
40 squares. Calling it before watching video or reading comments
What grade is the formula taught again? Just curious.
40 in the main square and plus 1 cause the image is a square as well.
Right! But, i would have said there is only 1 3×3 square, unless you want to count some of the rows and columns again and look at it from a different side. And i would have said there are 4 2×2 squares...for example, when you start from the upper left side why would you count the 2nd column again?
I know it's trivial, but for your proof by induction to be complete, you need to start to prove it for n=1
For the plain grid, what about n.(n+1).(2n+1)/6 ?
16+9+4+1 (small squares removed) + 2*(4+1) (extra squares)
The true answer: A LOT!
41 because the question contains the word "squares"
63 not even close
+Georgie Rosales thats how many genders Google thinks there are
4 words of squares ahaha
Yep ! There are 40 squares !
Noel Walters it's 41 because he didn't count a 2×2 square in center
I have a rectangle and I would like to know how to calculate the dimensions for squares in multiples of 3. I need 3 wide, how many tall I need depends on the volume required to be covered in the rectangle. Hope you can help thankyou.
Squares of side length 1/2 = 8
+
Squares of side length 1 = 18
+
Squares of side length 2 = 9
+
Squares of side length 3 = 4
+
Squares of side length 4 = 1
Total = 40.
And we could use the following formula to calculate number of squares in nxn grid.
1^2+2^2+3^2+...+n^2 = n(n+1)(2n+1)/6
My English teacher just came in the room and said" how many squares are they time starts now" I was like math?
The answer is 40, if I’m correct we have to count carefully so take the 2 small squares in the middle away so we can walk through this clearly, we have 1 big square (4x4) and we can only make 1 of that. Next we have 3x3 you can make 4 squares with these 3x3. Now we have 2x2 you can make 9 squares with those 2x2. Now, we can count the 1x1 you can make 16 of. So we now add 1+4+9+16=30.
Next, we can add those squares back from the middle that we took away. Now we can count that there are 2 big squares. Now the small squares, if there are 4 in each and there’s 2, that makes 8
So 30+2+8=40. Y’all welcome! 🤗
Is there a methid using permutations or combinations?
40, this made my brain hurt beyond comprehension because every time I think I already added one to whatever count I was on, I'd restart again.
I’ve been counting the pixels on my screen for a while now....
Lol
I'm going to referencing your video three moving squares in three moves for more of a clarification of what I mean. You have really small red squares on all the brown lines. Those red squares are the same size as white ones in this video. Thanks
can someone explain it to me how the formula 1^2+2^2+3^2..…n^2=n(n+1)(2n+1)/6 is used in the problem???
pleaseee because its a little bit confusing
Plot twist.: there are actually 0 squares in the picture because all of them are rectangles with an aspect ratio of 1.0001:1.
Does that include rectangles cause all rectangles are squares but not all squares are rectangles?
40, I used the trusty old formula of starting at 1 and adding 1 at a time until I was done.
why do people dislike this?
dumb people hate hard things.
Idk
Sam Frieder, PhD Sexist?
Too easy
because it's not correct
31
I had this problem a while back ago, pretty sure the answer was 40
What is next draw this numbers geometry in the grid 04,07,26,38,45 ???????
At first I was like, there's totally 17 squares, but had no idea it was a 90° square lol
0:00 - 36 my guess, probably some hidden gems in there
I had 32 until you got rid of the squares in in the middle at 0:18, after that I had 40.
I think 31
Now count how many rectangles. I get 118.
thanks man you saved me from explaining a riddle in english class. yea english class
defaulty boi
(4^2+3^2+2^2+1^2)+
[2(2^2+1^2)]
= 40.
Elson Ngai hi
Thankkkkk Youuuuuuu veryyyyyyy muchhhhhh 🥳🥳🥳🥳 I was having the same question
The two middle squares aren't necessary for the interesting part...
Nice one though...
Why wouldn't you count the other squares? Like the 1x2 and the 2x3 squares etc. aren't they also squares? I thought those also counted so I got to something like 86 before I stopped cause I couldn't bother
A square is a quadrangle with sides all the same length, so a 1*2 would be a rectangle, not a square.
Rohen Giralt Oh allright, in my language a square is just any shape with 4 sides
Very thorough and well explained!
But why not also give the closed form of that sum?
S₂(n) = ∑ᵢ₌₁ⁿ i² = ⅙n(n+1)(2n+1)
S₂(4) = ⅙·4·5·9 = 2·5·3 = 30
UA-cam formatting is like *dies*
What do u mean? 😂
ffggddss mi so FYIdubai
The problem statement is under specified. What counts as a square? Can it contain only white space? Can it contain other lines? We don't know until the "solution" is presented.
Of course people get it wrong when there is more than one valid answer.
why is there 2 fewer squares of size 2x2?
Best idea
36 i believe
no more
what is love? baby dont hurt me.. dont hurt me...
Geometry question : How many square are in this picture?
Me: A lot
Mathematics: 40
Also me: ah yes yes 40
Thank you
Easy peasy. I found the correct answer in about 10 seconds.
Yes I solved it correctly. who did click on like button.
Yes got 40
isnt there a 2*2square right in the middle
Rectangles: 118
Squares: 40
The argument why there are 2n-1 new 2x2 squares and so on isn't quite verbose...
(Also technically the base case is missing.)
But considering the comments most viewers care more about the number of squares. ;-)
I know an easier way. For a n x n square the solution to the number of squares is ((n)(n+1)(sum of two previous numbers))/6. Example: 4x4 square: ((4)(5)(9))/6 = 30. 2x2 square: (2x3x5)/6 = 5. It's easier to do than than square sums as multiplication cancels out.
+Mindyourdecisions
1/3n^3 + 1/2n^2 +1/6n then add 10 for 2 middle squares!
Here's a riddle.... What is the probability of this channel finding a challenging riddle?
Solution:
Well there are a couple of methods to find the correct answer
Method1: counting every riddle so we have 0challenging riddles and 73635 easy/bullshit riddles.... I might have miscounted that but it doesn't matter because 0/X is 0... So we can't expect any challenging riddles
Method2: praying for better riddles.... We will get the result but this method takes a looooong time to work... Just like the method in this video.... It takes forever.... LITERALLY
Another back water reverse thinking Rusky trying to act special for attention - LOL
1^2 + 2^2 + 3^2 + ... n^2 can also be written as (2n^3 + 3n^2 +n) / 6. Dont believe it? try it out yourself :)
There are 17 when the little squares are in the middle the ones that the little squares are in are like half a square
Superb
There are more ''big middle'' squares than the 2 you mentioned so much more ''small middle'' squares to count...
I counted 36.
Well, I guess, I'll go back on square one.....
1:57 I had discovered that method 2 years ago
1+4+9+16=30
It’s all the square numbers.
30+2=32
The other squares.
32+8=40
All the mini squares.
i always forget the 3x3 dammit
I forgot until someone said 3x3. I counted 40
It is always ok
16 individual and nonintersecting squares, and I counted 40 ways to make squares.
can we we with trianhles also
Yes there's a different video on it in his other videos. It's been 7 years but I'll be glad to help you bhaiyya
"how many squares you can make out of the image"
by you *making* all the squares you can make you get to 40... but again... the true square is 1 (X), inside that one big Square your counting what forms it to be that value.
so again. all the Squares you can see is 40 but it's not equivalent to X if you add them up...
If you add up all the Squares (of the same size ignoring the little ones at the center you) there's 16 in total which is equivalent to (X) the big square. imagine this... X=to 16... "fractions" that make up for the hole piece (of square) if you divide 16 with 16 you get one which is equal to "the big square".
soo again the answer can differentiate of how many "Exact" Squares there are... "but" the Big one is equal to the 16 smaller Squares.
Key point:
you can only get to 40 by "ignoring" the exact value of X, by adding all the different square shapes "you make" and adding them up in a way it's not equivalent to the exact value of X Square.
I've counted 40, and I must say that this is one of those easy tests for small children. I don't know why I even bother clicking these kind of videos. Maybe I just want to have false sense of being smart, no?
It seems like there are more squares that you missed if. you count the the optical illusion squares that happen inside the grid. There is a tiny Square at each line intersection except for the four corners of the largest square. Please disregard is this comment is annoying.
omg I guess 39! Im done with riddles
now my brain is square
shit, I counted the rectangles as well, I got like 110 or something. I didn't know the term "square" was only "4-gons" with equal side lengthes. Now I feel like a complete dummie...
i had 26
I got 37 lol
.
I got 24
38
i got 27 :(
Got 45, writing this before the answer...
48 OR 44 OR 40
Edit:FORGOT THE 12 SQUARES OR 8 OR JUST 4 AND I ADD THIS IF n= 6.9282032303 the answer is 48 then if n= 6.3245553203 the answer is 40 and if n= 6.6332495807 the answer is 44
Yay got 40 by method 1
This was really easy for me.
What I really want to know is how to do those stupid ass triangle ones.
Thanks😆😆😆
That is so bogus it is silly. It all revolves around how you define "a square." In my mind, a "square" has four equal length sides with 90 degree corners that contains *nothing else*. By *that* definition there are 16. Once again, semantics.
Per definition, a square has four equal length sides with 90 degree corners. The last part you said is mathematically not required for an object to form a square.
This is not semantics, how you call it; a square is a well-defined object and therefore, the picture contains 40 of them.
If you have to remove squares to count , your changing the picture and creating a false narrative . The two squares you removed made the others obsolete and they are part of the picture . Perspective is everything . In all actuality there are 21 squares without an overlap . Once you add the overlap you can't just remove it ; It's part of the picture .
I felt good about that. I missed two 2x2s in my initial count so I was close
Boy, did I miss that one.
The correct answer should be 32, because the 8 1x1 squares in the inside columns are actually L shapes and not squares. It's all a matter of perspective. If you don't take the picture apart the answer is 32.
it is: n (n+1)(2n+1)/6
40.
Woo, got it!
but in my i.q. puzzle book it says 44