### Exhaustion

Find the positive integer solutions of the equation (1+1/a)(1+1/b)(1+1/c) = 2

### Dodgy Proofs

What is wrong with these dodgy proofs?

# Code to Zero

##### Stage: 5 Challenge Level:

Find all the 3 digit numbers such that by adding the first digit, the square of the second digit and the cube of the third digit you get the original number, for example $1 + 3^2 + 5^3 = 135$. Can you find ways of reducing the search so that you do not need to test 900 cases?

[This problem appears in Ken Follett's spy thriller of the same name].