Identical small triangles are used to build up a big triangle. The top row holds 1 small triangle, the second row 3, the third row 5, and each new row holds 2 more than the row above it. How many small triangles are used in a big triangle of 8 rows?

The rows hold 1, 3, 5, 7, 9, 11, 13, 15 triangles. Adding them gives 64, and there is a shortcut worth remembering: the first $n$ odd numbers always add up to $n\times n$, so 8 rows give $8\times 8=64$. The traps: 36 adds 1 + 2 + 3 + … + 8 as if each row grew by only one triangle; 81 is $9\times 9$, from counting one row too many.