Henry Ernest Dudeney/Modern Puzzles/81 - Pussy and the Mouse/Solution

by : $81$

 * Pussy and the Mouse

Solution
Barrel no. $4$.

Proof
Let $n$ be the count.

Let $m$ be the number of the barrel the mouse is in.

By the method of counting, all we are concerned about here is the value of $n \pmod 8$.

If $n \pmod 8 = 0$, then $m = 2$.

If $1 \le n \pmod 8 \le 5$, then $m = n \pmod 8$.

Otherwise $m = 10 - n \pmod 8$.

Here $n = 500$, and so $n \pmod 8 = 4$.