On a square gameboard that is divided into n rows of n squares each, k of these squares do not lie along the boundary of the gameboard. If k is one of the four numbers 10, 25, 34, or 52, what is a possible value for n?

Question

Zaiden

Mathematics

22 May, 08:31

On a square gameboard that is divided into n rows of n squares each, k of these squares do not lie along the boundary of the gameboard. If k is one of the four numbers 10, 25, 34, or 52, what is a possible value for n?

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Answers (1)

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Derrick Melendez · Answer 1

Answer: 7

Step-by-step explanation:

-if y is the width and the length of area k (see diagram), the difference between n and y is of 2 square sides, one at each side of y.

-therefore, assuming that n is a whole number and that there aren't half squares, y must be a whole number too because, as previously said, n-y = 2 so y = n - 2

-the only perfect square amongst the values for k you listed is 25, so taking n and y as whole numbers the only possible value for k is 25

-therefore y is 5 and n is 7 because n-y = 2 so y + 2 = n