Wednesday, August 01, 2012

Square Grid Puzzle: How Many Squares Do You See?

How many squares do you see in this picture:
This puzzle has been going round the internet, and here's my analysis


I see 40:
  • 8 tiny ones, in two 2x2s
  • 18 regular (4x4 plus 2 in middle)
  • 4 2x2s one at each corner
  • 4 2x2s centered on each side
  • 1 2x2 in the middle
  • 4 3x3s one at each corner
  • 1 4x4
--------------
EDITTED:
Ok, some people don't see why there's 9 2x2 squares. Here they are with color to help:
The first 4, that everyone sees
One in the middle, easily seen

2 more

And the last 2!


25 comments:

Anonymous said...
This comment has been removed by a blog administrator.
Anonymous said...

Mate, you have double counted 8 2x2 squares there is only 9 in total

Anonymous said...

Mate, you have double counted 8 2x2 squares there is only 9 in total

rewinn said...

@Anon 9:49 - not really.
We agree there are 9 2x2s.
So:
1 4x4
4 3x3s
9 2x2s
18 1x1s
8 tiny squares

1+4+9+18+8=40

Anonymous said...

There are 36 squares all together. There are only five 2x2 squares couning the one in the middle.

rewinn said...

Hi @Anon 9:05.
There are 9 2x2s. To show this, I've added pictures to the post coloring them in.

Boris said...

Correct answer is 40 - you forgot the 4 3x3's ...

Anonymous said...

There are 40. Not less, not more.

Ms. Bynoe said...

you don't count the 4 3x3 squares???

Avinash Deshmukh said...

very easy
(4²+3²+2²+1²)+(8+2)=40

Anonymous said...

40

Anonymous said...

3x3's should not be included. 4 sides may be the definition of squares but does not follow the same pattern as the rest of the puzzle.

Anonymous said...

A square is a square, regardless of its size. 3x3 included. There's so a 4x4 square, shall we exclude it as well???

Anonymous said...

A square is a square, it has all equal sides, THAT is pattern, so yes, 3x3's DO count and the final answer IS 40.

Kram Nosned said...

I swear I one time counted 40 but it was after a very long day. 40 is easily found if one only thinks inside the box...

Kram Nosned said...

I swear, one time I counted 41 but 40 squares are easily found, if one only, "Thinks Inside The Box"...

Todd Furse said...

I counted 40 then added 1 for the guy counting it. Oops, I revealed my true nature.

David Carmona said...

NO ONE COUNTED THE 4x4 SQUARE HOLDING ALL THE SQUARES.... BUNCH OF IDIOTS!!!!

Randy Winn said...

Well, not "NO ONE". Actually, several replies explicitly include it, e.g.

"1 4x4
4 3x3s
9 2x2s
18 1x1s
8 tiny squares

1+4+9+18+8=40"

Anonymous said...

http://krexy.com/how-many-squares

Anonymous said...

37 Black line + 4 orange big + 4 green big + 4 blue big + 4 red big + 2 small orange + 2 small green + 2 small blue + 2 small red = 61 squares...

Anonymous said...

37 Black line + 4 orange big + 4 green big + 4 blue big + 4 red big + 2 small orange + 2 small green + 2 small blue + 2 small red = 61 squares...

Randy Winn said...

My friend, the Orange squares include the black line squares and overlap with the green squares - so a count of 61 requires double-counting.

Anonymous said...

Some of you are counting the colors... The colors are for illustration purposes only. To show you the actual squares.

Anonymous said...

What about the 9x9 from each corner?