Question

A regiment of soldiers when formed into a solid square has 16 men less in the front row than when formed into a hollow square 4 deep. Find the number of soldiers?

Answer 1

Answer:

Okay, so this is actually very simple if you stop and think about it.

You obviously know that the number of soldiers must be a multiple of 10, 15 and 25.( Only then, can they be drawn into lines of 10, 15 or 25).

So now the possibilities are multiples of 150 ( LCM of 10,15,25). ( 150 = 2*3*5*5

As 10 is present and your final answer needs to be a perfect square, you need another factor of 2.

Also as 15 is present you need a factor of 3.

Therefore you multiply 150 by 2 and 3 to get 900 which is your answer.

900 = 2^2 *3^2*5^2