Problem #PRU-100448

Problems Algebra and arithmetic Number theory. Divisibility Division with remainders. Arithmetic of remainders Odd and even numbers

Problem

After the Mad Tea-Party, the Hatter was so excited that he decided to cool down by going on a short walk across the chessboard. He started at position a1, then walked around in steps taking each step as if he was a knight, and eventually returned back to a1. Show that he made an even number of steps.