# The Solution to the Matchstick and Square Puzzle

It’s been three months since I posted the Matchstick and Square puzzle. According to one of the comments, it’s already causing household arguments., so I think it’s high time that I post my solution. There is no key to the puzzle, I only found it on a Facebook Page.

Please check if my solution below is correct. 🙂

Solution

There are nine  $1 \times 1$ squares.

There are five $2 \times 2$ squares.

There is one $3 \times 3$ square.

There is one $4 \times 4$ square.

Therefore, there 16 squares.

## 20 thoughts on “The Solution to the Matchstick and Square Puzzle”

• That is what I got the first time I looked at it but then I went to explain it to someone later that day and I couldn’t come up with the same result and it’s irritating me now. Can you message me how you got 21 if you can remember it. Thanks!

1. There are actually 18 squares. There are 9 1×1. 5 2×2. 1 3×3. 1 4×4. Also there are two rectangles, and if we remember back to our good old geometry days rectangles are squares but squares aren’t rectangles

• In geometry, a square is a regular quadrilateral, which means that it has four equal sides and four equal angles. a square is a special kind of rectangle, it is one where all the sides have the same length. Thus every square is a rectangle because it is a quadrilateral with all four angles right angles. However not every rectangle is a square, to be a square its sides must have the same length.

2. Rectangles are considered squares, but not the other way around. Therefore, your solution is not correct.

• Wrong. Squares are rectangles where all 4 sides are the same length. Thus a 2×1 rectangle is not considered a square

3. 0 squares because you have to have right angles to have a square and right angles have to have to common points. The lines do not touch, now if you said how many squares can you draw by following the lines, I would say 16.

• Jill above is correct and the rest are wrong. Since the sides don’t actually touch there are NO geometric shapes, thus NO squares. The correct answer is ZERO.

4. It is the other way around. All squares are rectangles but not all rectangles are squares. Lets not over think this, there are 16. While we are at it , there is no such thing as big foot.

5. Time to square off on this and get everything squared away ;P

6 – there are 36 matches, therefore the picture contains 6 perfect square roots: 1(2), 2(2), 3(2), 4(2), 5(2), 6(2)
6 – the picture contains 5 Carpenter Squares and 1 T Square.
16 – 1×4×4, 1×9×9, 5×2×2, 9×1×1
25 – A rectangle of infantry was referred to as a square, historically.
48 – if you lay two pieces of wood that are straight and parallel to each other they are said to be square. There are 48 parallels.
164 – 2 consecutive 90 degree angles, such as on a board, is said to be square.

Everything I listed falls into the definition of square in the dictionary.
The total is 265

6. How about 22? You forgot to include the tiny squares formed at the interstices of the 1-by-1 squares – they are four-sided, too – if you are going to accept imperfect and slightly open squares, as you have with the larger configurations.