Maths Olympiad Prep

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Combinatorics Difficulty 4.9 AIME Find the answer Netherlands

A chess board consists of 8×88 \times 8 squares. A knight is placed on a corner square. The knight makes jumps of either two squares horizontally and one square vertically, or two squares vertically and one square horizontally. On each square of the chess board, we write down how many jumps the knight needs to reach it.
Which number did we write down most often?
A) 2 B) 3 C) 4 D) 5 E) 6

This was a multiple-choice question, but the options didn't survive into the source we have. The answer given is C, and the solution below works it through.

Solution

C) 4

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Source: MathNet, licensed CC-BY-4.0. Statement and solution reproduced as published; topic and difficulty added by this site.