### Code to Zero

Find all 3 digit numbers such that by adding the first digit, the square of the second and the cube of the third you get the original number, for example 1 + 3^2 + 5^3 = 135.

### Dodgy Proofs

What is wrong with these dodgy proofs?

# Exhaustion

##### Stage: 5 Challenge Level:

Find the positive integer solutions of the equation

$\left(1 + \frac{1}{a}\right)\left(1 + \frac{1}{b}\right) \left(1+ \frac{1}{c}\right) = 2.$

This problem was taken from the Hungarian magazine KoMaL. There are many other challenging problems in English on the KoMal website.