face book counting squares puzzle

The EASY Visual Solution to the FaceBook Counting Sq uare Puzzle

Dedicated to that smart guy who kept getting the wrong answer. (You know who you are!)

Solution by Margaret D.

WTF?

There’s that *#@% puzzle you couldn’t solve right again!!

It’s ok. You’re going to survive this. I made it so simple that a 3rd grader could follow it.

That is always my goal when I explain stuff, so don’t take it TOO personally.

I mean, I’m sure you still belong in MENSA.

Pre-amble: So, you know the drill. Count how many squares are there are in this puzzle!

Safe bet#1: The easiest, most fail-safe method is to break them down into groups (categories) and count how many there are in each group. For example, how many squares are made of 4x4 blocks? How many squares are composed of 3x3 blocks? Etc.

Safe bet#2: count methodically in a clockwise fashion starting in the upper left corner to insure that no squares are missed.

Safe bet#3: I will keep a running count in the mini-worksheet on the following slides to insure we don’t lose count as we go along.

Just keep clicking to follow along in this slide presentation and you’ll see everything I just said above, step-by-step. No need to memorize it!

It’s still there …

It’s ok. You’re going to survive this. Really!!

Using big blocks

Using little blocks

4x4’s 1 0

3x3’s

2x2’s

1x1’s

Subtotals

COUNT SQUARES THAT HAVE 4 BLOCKS UP AND 4 BLOCKS ACROSS (4X4’S)

This one is too easy!! The entire big square is the only one that is a “4x4”. (the 2 overlaid squares have been temporarily removed because they are 2x2’s).

Using big blocks

Using little blocks

4x4’s 1 0

3x3’s 1

2x2’s

1x1’s

Subtotals

COUNT SQUARES THAT HAVE 3 BLOCKS UP AND 3 BLOCKS ACROSS (3X3’S)

1st one …

Using big blocks

Using little blocks

4x4’s 1 0

3x3’s 2

2x2’s

1x1’s

Subtotals

COUNT SQUARES THAT HAVE 3 BLOCKS UP AND 3 BLOCKS ACROSS (3X3’S)

2nd one …

Using big blocks

Using little blocks

4x4’s 1 0

3x3’s 3

2x2’s

1x1’s

Subtotals

COUNT SQUARES THAT HAVE 3 BLOCKS UP AND 3 BLOCKS ACROSS (3X3’S)

3rd one …

Using big blocks

Using little blocks

4x4’s 1 0

3x3’s 4 0

2x2’s

1x1’s

Subtotals

COUNT SQUARES THAT HAVE 3 BLOCKS UP AND 3 BLOCKS ACROSS (3X3’S)

4th and final 3x3.(There are no 3x3’s in the “little block” category).

Using big blocks

Using little blocks

4x4’s 1 0

3x3’s 4 0

2x2’s 1

1x1’s

Subtotals

COUNT SQUARES THAT HAVE 2 BLOCKS UP AND 2 BLOCKS ACROSS (2X2’S)

1st one …

Using big blocks

Using little blocks

4x4’s 1 0

3x3’s 4 0

2x2’s 2

1x1’s

Subtotals

2nd one (going clockwise) …

COUNT SQUARES THAT HAVE 2 BLOCKS UP AND 2 BLOCKS ACROSS (2X2’S)

3rd one (still going clockwise)

COUNT SQUARES THAT HAVE 2 BLOCKS UP AND 2 BLOCKS ACROSS (2X2’S)

Using big blocks

Using little blocks

4x4’s 1 0

3x3’s 4 0

2x2’s 3

1x1’s

Subtotals

4th one (still going clockwise)

COUNT SQUARES THAT HAVE 2 BLOCKS UP AND 2 BLOCKS ACROSS (2X2’S)

Using big blocks

Using little blocks

4x4’s 1 0

3x3’s 4 0

2x2’s 4

1x1’s

Subtotals

5th one (still going clockwise)

… (click mouse)

COUNT SQUARES THAT HAVE 2 BLOCKS UP AND 2 BLOCKS ACROSS (2X2’S)

Using big blocks

Using little blocks

4x4’s 1 0

3x3’s 4 0

2x2’s 5

1x1’s

Subtotals

6th one (still going clockwise)

COUNT SQUARES THAT HAVE 2 BLOCKS UP AND 2 BLOCKS ACROSS (2X2’S)

Using big blocks

Using little blocks

4x4’s 1 0

3x3’s 4 0

2x2’s 6

1x1’s

Subtotals

7th one

COUNT SQUARES THAT HAVE 2 BLOCKS UP AND 2 BLOCKS ACROSS (2X2’S)

Using big blocks

Using little blocks

4x4’s 1 0

3x3’s 4 0

2x2’s 7

1x1’s

Subtotals

8th one (DONE going clockwise, but ...

COUNT SQUARES THAT HAVE 2 BLOCKS UP AND 2 BLOCKS ACROSS (2X2’S)

Using big blocks

Using little blocks

4x4’s 1 0

3x3’s 4 0

2x2’s 8

1x1’s

Subtotals

Don’t forget the 9th one in the middle! We are now done counting 2x2’s composed of large blocks. Now, to count 2x2’s composed of small blocks (next slide).

COUNT SQUARES THAT HAVE 2 BLOCKS UP AND 2 BLOCKS ACROSS (2X2’S)

Using big blocks

Using little blocks

4x4’s 1 0

3x3’s 4 0

2x2’s 9

1x1’s

Subtotals

1st small-blocked 2x2 square.

COUNT SQUARES THAT HAVE 2 BLOCKS UP AND 2 BLOCKS ACROSS (2X2’S)

Using big blocks

Using little blocks

4x4’s 1 0

3x3’s 4 0

2x2’s 9 1

1x1’s

Subtotals

2nd and final one of the small blocked 2x2’s.

COUNT SQUARES THAT HAVE 2 BLOCKS UP AND 2 BLOCKS ACROSS (2X2’S)

Using big blocks

Using little blocks

4x4’s 1 0

3x3’s 4 0

2x2’s 9 2

1x1’s

Subtotals

Let’s just use MATH to count these easy ones up. There are 4 large blocks vertically and 4 across. So, 4x4=16 large atomic-level blocks! I’ve made all of them a different color JUST IN CASE you are getting dopey on me. You can count all of the different colors if you don’t believe me. Remember, here, we are only counting the LARGE blocks that are at the atomic level (1x1).

Note: Don’t make the mistake of double-counting the overlay squares that are straddling the bigger ones and are composed of small 2x2 blocks! We will count their little 1x1 blocks on the next slide.

COUNT 1x1’s . These are the atomic level (single) BIG blocks.

Using big blocks

Using little blocks

4x4’s 1 0

3x3’s 4 0

2x2’s 9 2

1x1’s 16

Subtotals

COUNT 1x1’s . These are the atomic level (single) LITTLE blocks.

Using big blocks

Using little blocks

4x4’s 1 0

3x3’s 4 0

2x2’s 9 2

1x1’s 16 8

Subtotals

4

8

1 2

3

5 6

7

So, a total of 8 little blocks at the atomic level.

SUBTOTAL and TOTAL the NUMBER OF SQUARES

Using big blocks

Using little blocks

4x4’s 1 0

3x3’s 4 0

2x2’s 9 2

1x1’s 16 8

Subtotals 30 10

Answer to the puzzle: 30 + 10 = 40 total squares!

To J.H.: I hope you appreciate me explaining this so clearly. I could use a pat on the back. Or, a pat just about anywhere from this guy.

Oh, almost forgot to tell you! There was a catch to receiving this solution! Yep, totally forgot to mention it, but you may only remain in MENSA if you hunt down this man and bring him to me.

Good luck! He’s in Italy somewhere, probably. Goes by the name of Gabriel Garko.

Look at him. Poor guy. He’s so bummed because he couldn’t solve the puzzle, either. So, I just HAVE to explain it to him. Pronto! And, privately!!

Thanks!! I knew you’d understand!!