For example, adding up all the numbers in the first 5 rows of Pascal’s triangle gives us the 5th Mersenne number, 31 (which is 1 less than 2 to the power of 5).

Since each row has an additional number in it than the previous, writing out the numbers in such a way results in a triangular shape, as pictured below. Diagram credits to the author/The Daily Campus.

Rows zero through five of Pascal’s triangle. The pattern continues on into infinity. Two of the sides are filled with 1's and all the other numbers are generated by adding the two numbers above.

Here's another number game you can do using Pascal's Triangle. I don't know why I'm so into numbers today, but I have a cold, so if you'll just indulge my sick predilections maybe I'll manage to ...