Problem
First name
10Ma1
School
Woodrush High
Country
Age
14
Email address
jmclaughlan@woodrushhigh.worcs.sch.uk
Initially we looked at the fact that n = a^2 - b^2 where n is the total number of soldiers, a is the side length of the outer square and b is the side length of the inner square.
For 960 soldiers we found 5 solutions for a symmetrical hollow square.
These pairs were:
31 and 1
32 and 8
34 and 14
38 and 22
46 and 34
We then looked for patterns and noticed all but 1 pair had a difference in multiples of 4.
We then decided that all multiples of 4 would work for the value of n.
We also found that a+ b was always a factor of n