Sunday, March 22, 2015

Just for Fun... How Many Squares...

I posted on my personal Facebook timeline the following quiz:

Want to know how many squares are actually there? Just continue after the jump...

I originally counted 38 but as I was grabbing the puzzle to post here I discovered I was incorrect. The actual number is 40! Can you see them all? I've broken them down for you.

First, I counted all the individual squares:
 Next, I counted the 4x4 square groups in the four corners:
 On the third pass, I expanded to 3x3 square groups:
 For the fourth pass, I counted the 2x2 squares in the middle, going vertically:
 The fifth pass counted the 1x1 squares in the  center of the main square:
 The sixth pass counted the small individual squares created where squares 28 and 29 were divided by the borders of squares 2,3, 6 and 7 (for square 28) and squares 10, 11, 14 and 15 (for square 29.) I then counted the overall square as 38 and thought I was done.
That was when I discovered that, although I had counted the 2x2 squares in the middle, going vertically, I had neglected the 2x2 squares in the middle, going horizontally. That gives us 40 squares.

Not bad for a sleepy Sunday morning...

1 comment:

  1. WHEW! Glad that one is figured out. It was just enough to stimulate my mind. Now I am going to study the rest of the day. Thank you :) Have a great day!!