This is a recent Alex Bellos problem that supposedly can be solved by 12-year-olds!

“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.

**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*

Which agent will agent 007 get her present from?”

See the Spy Gift Problem for solutions.

**(Update 9/7/2024) Rigorous Solution**

It turns out that the solution to “The Umbrella Problem” provides an approach for a rigorous justification of Alex Bellos’s solution to the “Spy Gift Problem”.

Oscar RojasI solved using modular arithmetic:

x-7≡7-(x+1) (mod 9)

2x≡13≡4 (mod 9)

x≡2 (mod 9)

then x=2 is the only solution.