# Advent calendar 2020

## 24 December

There are six ways to put two tokens in a 3 by 3 grid so that the diagonal from the top left to the bottom right is a line of symmetry:

Today's number is the number of ways of placing two tokens in a 29 by 29 grid so that the diagonal from the top left to the bottom right is a line of symmetry.

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Either both pieces must be on the diagonal, or one pieces is in the lower right half and the other is in the reflected position in the upper right half.

There are \(\left(\begin{array}{c}29\\2\end{array}\right)=406\) ways to pick two squares on the diagonal. There are 406 squares below the diagonal.

Therefore there are 406+406 = **812** ways to arrange the pieces.