Today’s problems come from Axiom Maths, a charity that that takes high-attaining primary school children and provides them with maths enrichment during secondary school.

One of Axiom’s main activities is to organise ‘maths circles’, in which small groups of pupils get together to tackle fun problems. Such as the ones below, which are aimed at children aged 11/12, and form the basis for further explorations.

1. Backwards multiplication

What four-digit number reverses itself when multiplied by 4? As in, what are the digits a, b, c and d such that the number abcd x 4 = dcba?

(In this problem, the letters a, b, c and d all stand for different digits.)

2. Really secret Santa

A group of nine secret agents: 001, 002, 003, 004, 005, 006, 007, 008 and 009 have organised a Secret Santa. The instructions are coded, to keep the donors secret.

Agent 001 gives a present to the agent who gives a present to agent 002

Agent 002 gives a present to the agent who gives a present to agent 003

Agent 003 gives a present to the agent who gives a present to agent 004

and so on, until

Agent 009 gives a present to the agent who gives a present to agent 001