Chess

Probability Level 3

How many ways are there to go around from one corner of the chess board to another ?

Note:- You can only go up, right.


The answer is 12870.

Aayush Mani by Aayush Mani , 21, India

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1 solution

Aayush Mani
May 30, 2014

Formula for such problems is (m+n)C(m or n)

So here 8C8= 16!/8!*8!=12870

1 Helpful 0 Interesting 0 Brilliant 0 Confused

But you only have to go 7 over and 7 up, the problem is wrong

Nathan Ramesh - 7 years ago

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The problem does specify the term "corner" which is distinct from "corner space", so the problem is referring to the vertices on the chess board rather than the spaces. So the required amount of moves is 16 rather than 14

Caleb Townsend - 6 years, 4 months ago

A small error.... It should be 16C8. Anyways, a nice problem!:)

Samarpit Swain - 7 years ago

It seems to me that your answer is not correct. For to get from the lower left corner to the upper right you need to make 14 steps not 16. And you should get 14!/7!*7!. Please, let me know where I am wrong.

Сергей Кротов - 6 years, 12 months ago

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Your solution is correct if we are talking about spaces on the chess board; however, we are talking about the corner vertex itself rather than the space on the board.

Caleb Townsend - 6 years, 4 months ago

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