How many musicians were in the band?

Question

A military band was marching in formation. At first, the marchers formed a perfect square with an equal number of columns and rows, but then changed formation and became a rectangle with 5 more columns than before. how many musicians were in the band?

Answer 1

Well, the number has to be a perfect square and a multiple of 5.

 

Start with 5 x 5. 25 musicians can't make 10 columns.

 

10 x 10. 100 musicians can't make 15 columns.

 

15 x 15. 225 musicians can't make 20 columns.

 

20 x 20. 400 musicians make 25 columns of 8. 

 

There are 400 musicians.