problem

### Particularly general

By proving these particular identities, prove the existence of general cases.

problem
###
Particularly general

By proving these particular identities, prove the existence of general cases.

problem
###
Cubes within Cubes revisited

Imagine starting with one yellow cube and covering it all over with
a single layer of red cubes, and then covering that cube with a
layer of blue cubes. How many red and blue cubes would you need?

problem
###
Partitioning revisited

We can show that (x + 1)² = x² + 2x + 1 by considering
the area of an (x + 1) by (x + 1) square. Show in a similar way
that (x + 2)² = x² + 4x + 4

problem
###
Powerful Factors

Use the fact that: x²-y² = (x-y)(x+y) and x³+y³
= (x+y) (x²-xy+y²) to find the highest power of 2 and the
highest power of 3 which divide 5^{36}-1.

problem
###
Binomial

By considering powers of (1+x), show that the sum of the squares of
the binomial coefficients from 0 to n is 2nCn