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Logic Level 1

There is a knight on a chessboard, on h1. It makes x x moves before returning back to the square it started. What class of number does x x necessarily belong to?

even number odd number

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Arka Das by Arka Das , 20, India

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7 solutions

Kyle Coughlin
Jun 22, 2015

If you think of a chess board, a knight will always jump from a light square to a dark square or vice versa. Therefore, if you start on a light square, you always need to make 2x jumps to get to the same color square you started on.

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There are both light and dark squares that a knight starts on, and the nearest knight starting square to h1 is dark while h1 is light. To get to that square would necessarily take an odd number of jumps.

Matthew Helm - 3 years, 5 months ago
Uttkarsh Kohli
Jul 24, 2015

he reverses his every move he does to get back on the same position so....the answer is 2x

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Feathery Studio
Jun 21, 2015

Every other move reverses the move that was just did, therefore, it must be 2 x 2x , or an even number.

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But it said "before returning back to the square it started" so i think it must be a 2x -1, or an odd number

Rian Hasiando Silaen - 5 years, 11 months ago
Finn C
Apr 26, 2016

I want to point out that the only options that would work are odds and evens because odds are prime numbers, and odds and evens are composite numbers.

Also the answer is 2 because you can move your knight to any square then move it back. However, 2 is also a prime number as well as an even number. Challenge Master can you explain why that is? Is there something I missed?

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Moderator note:

The question is "What class of number does x x necessarily belong to".

Since these 4 sets are not subsets of each other, the answer must be unique. For example, x = 4 x = 4 is a possibility, and that is not a prime number.

Patrick Prochazka
Aug 13, 2015

Each time the knight jumps, it switches colour. Therefore, to return to the same square (or any square of the same colour) it needs to jump an even number of times.

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I beileve the question need to rephrased the word "before" might be confusing someone would understand that the last move to get to initial square isn't included

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Tom Kearney
Jun 22, 2015

As the number of moves you have already taken will need to be doubled to get back to your starting position, the number will always be even.

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