The Mathsbombe Competition

2026 edition. From the people behind the Alan Turing Cryptography Competition.
Home Archive
The Problems
Problem 5
Released Wed 25th Feb 4:00PM
Problem 6
Released Wed 25th Feb 4:00PM
Problem 7
Released Wed 11th Mar 4:00PM
Problem 8
Released Wed 11th Mar 4:00PM
Solutions
Released Mon 30th Mar 4:00 PM

Problem 4

A robot is programmed to travel from the centre of a circle of radius 2026 by repeating the following three steps:

  1. The robot takes a step of length 1 in the direction it faces;
  2. If its current distance to the centre is not a whole number, then the robot turns so that the centre of the circle is directly to its left;
  3. If its current distance to the centre is a whole number, then the robot first takes a step of length 1 directly away from the centre and then turns so that the centre of the circle is directly to its left.
How many steps will it take for the robot to reach the edge of the circle? (The steps taken as part of directives 1. and 3. both count!)

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

What is 9 × 6 + 5?  

This problem was first solved on Wed 4th February at 4:02:49pm
Mathsbombe Competition 2026 is organised by the The Department of Mathematics at The University of Manchester.
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