Count the numbers of squares

Probability Level 4

This is a 8 8 x 8 8 square lattice,

For a 15 15 x 15 15 lattice

The total number of squares that can be formed using 4 points such that the squares can be of any orientation (for example the red and green squares shown in the 8x8 lattice) is 10 N 10N

Find N N


The answer is 420.

Shauryam Akhoury by Shauryam Akhoury , 18, India

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1 solution

Hana Wehbi
Nov 16, 2018

Let p = 15 p=15 and q = 15 ⟹ N p , q = 4200 = 10 × 420 ⟹ N = 420. q=15\implies N_{p,q}= 4200=10\times 420 \implies N=420.

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