There are **5** NRICH Mathematical resources connected to **Proof by exhaustion**, you may find related items under Thinking Mathematically.

Challenge Level

How many possible necklaces can you find? And how do you know you've found them all?

This article for primary teachers discusses how we can help learners generalise and prove, using NRICH tasks as examples.

These tasks provide opportunities for learners to get better at proving, whether through proof by exhaustion, proof by logical argument, proof by counter example or generic proof.

Challenge Level

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.

Challenge Level

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