Why aren't there 25? ... 10?

***************************

Take a square pyramid. Say it is of cannonballs or oranges. At the top there is one round shape. Below it there are four. Below that, nine.

Start unpacking. Fill a square with round shapes. First, one. After that, five. Going down a level further there will be fourteen.

Is there a level so that when all shapes are taken off and placed in a square, there is a completely filled four-sided shape?

There is. The only square that can be completely filled by deconstructing a pyramid has 576 elements. The deconstructed pyramid will have 24 levels.

The number 576 is the square of 24.

************************************

Find any three positive integers a, b, c such that

a

Note that

2

Use this if n is a multiple of 3 and 4 and n + 1 is a multiple of 5.

Smallest such n = 24.

2

(2

a = 2

b = 2

c = 2