The Mathsbombe Competition

2025 edition. From the people behind the Alan Turing Cryptography Competition.
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Problem 5

A group of children are playing with water balloons. First, they each select a position on the playground, and then at a signal, everyone throws their balloon at the person closest. If there are multiple people with minimal distance to them, they can freely choose who they aim at.

How many children were playing at most if in the end only 12 got wet, and everyone hit the person they aimed at?

To deter guessing without thinking, we ask that you also solve the following simple arithmetic problem before checking your answer:

What is five multiplied by nine, subtract four?  

This problem was first solved on Wed 26th February at 4:03:01pm
Mathsbombe Competition 2025 is organised by the The Department of Mathematics at The University of Manchester.
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