### 656 Halloween Tangram Puzzle Cats

It’s almost Halloween, and I was in the mood to make some cats out of tangram pieces. MANY cat tangram patterns exist as well as patterns for witches hats, bats, haunted houses, and candles. Black makes the shapes look like shadows so I made a couple of patterns here (using excel).

Tangram puzzles are made from the seven shapes in this square:

**How to fold and cut the tangram shapes** from a half-sheet of black construction paper or other paper. (Thank you Paula Beardell Krieg from Bookzoompa.wordpress.com for the link on making a square and advice on the rest of the directions):

- First make a square from the rectangular piece of paper, and visualize that square becoming the labeled square above.
- Fold the square from the top left corner to the bottom right corner and crease the paper on the fold. Unfold the paper.
- Partially fold the square from the top right corner to the bottom left corner allowing only the left half of the square to show a crease. This crease and the previous crease will form the two large triangles.
- Fold the bottom right corner to the point where the other creases intersect. This new crease will form the medium triangle. Unfold. Cut out the medium triangle.
- Refold the top right corner to the bottom left corner and crease the entire length this time.
- Cut along all the creases. You will then have cut out the two large triangles and be left with two odd pieces that look like this:

- Take the first odd piece and fold the longest straight edge so its endpoints meet. Crease and unfold. You should see a square and a small triangle. Cut them out.
- Place the newly cut small triangle over the second odd piece so that you see a small triangle and a parallelogram. Cut along the bottom edge of the small triangle so that you have a second small triangle and a parallelogram.

Now all seven pieces have been cut out and you can make your own cat or other fun creation!

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Here are some facts about the number 656:

656 is a palindrome in three bases:

- 220022 in base 3; Note: 2(243) + 2(81) + 0(27) + 0(9) + 2(3) + 2(1) = 656
- 808 in base 9; Note: 8(81) + 0(9) + 8(1) = 656
- 656 in base 10; Obviously, 6(100) + 5(10) + 6(1) = 656

656 is the hypotenuse of the Pythagorean triple 144-640-656. What is the greatest common factor of those three numbers?

- 656 is a composite number.
- Prime factorization: 656 = 2 x 2 x 2 x 2 x 41, which can be written 656 = (2^4) x 41
- The exponents in the prime factorization are 4 and 1. Adding one to each and multiplying we get (4 + 1)(1 + 1) = 5 x 2 = 10. Therefore 656 has exactly 10 factors.
- Factors of 656: 1, 2, 4, 8, 16, 41, 82, 164, 328, 656
- Factor pairs: 656 = 1 x 656, 2 x 328, 4 x 164, 8 x 82, or 16 x 41
- Taking the factor pair with the largest square number factor, we get √656 = (√16)(√41) = 4√41 ≈ 25.612497.

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