Inspired by the iconic amp from Spinal Tap that famously goes up to 11, today's puzzles delve into the intriguing mathematical world of this prime, two-digit palindrome. As the number of players in a football team, eleven holds a special place in both sports and numerical theory, offering a playground for curious minds to explore its unique properties.
Funny Formation: A Football Team Challenge
Imagine you are the coach of a football team with players wearing shirt numbers from 1 to 11, where the goalkeeper is assigned number 1. Your task is to divide the remaining ten players into three groups: defenders, midfielders, and forwards. The challenge is to arrange the team so that the sum of the shirt numbers in each group is divisible by 11. Can you find a valid example, or is this arrangement impossible? This puzzle tests your ability to balance numerical constraints within a real-world sports scenario, blending logic with playful strategy.
Pals or Not: The Palindrome Quest
When learning the 11-times table, many recall the simple pattern: 11 × 1 = 11, 11 × 2 = 22, up to 11 × 9 = 99, all of which are palindromes—numbers that read the same forwards and backwards. But what happens if we extend this multiplication up to 11 × 99? How many more results in this range are palindromes? For instance, 11 × 56 = 616 is one such example. This puzzle invites you to uncover the hidden symmetry in numbers, exploring beyond basic arithmetic to discover patterns that delight mathematicians of all levels.
Big Divide: Mastering Divisibility by 11
Less known than other divisibility rules, there is a clever method to test if a number is divisible by 11. Take the digits of the number and alternately add and subtract them, starting with a plus sign. If the resulting sum is a multiple of 11 (including zero), then the original number is divisible by 11. For example, with 132, we calculate 1 - 3 + 2 = 0, confirming divisibility. Using this rule, your challenge is to create the largest possible 10-digit number that is divisible by 11, using each digit from 0 to 9 exactly once. This puzzle sharpens your skills in number theory and strategic thinking, pushing you to optimise within strict constraints.
The Inspiration Behind the Puzzles
These puzzles are motivated by the fact that eleven is also the number of University Maths Schools in the UK. These innovative state sixth forms, attached to universities, cater to 16-19 year olds with a passion for mathematics. They offer a specialist curriculum designed to challenge students beyond standard courses, fostering deep engagement with the subject. Currently, nine schools are open, including King's and Imperial in London, Exeter, Liverpool, Lancaster, Cambridge, Leeds, and Aston. Schools at Durham and Nottingham received approval in December and will open in the coming years.
At University Maths Schools, playful mathematical exploration, like today's puzzles, is a daily occurrence. Applications for September 2026 are still open for Exeter, Liverpool, Lancaster, Leeds, Surrey, and Aston, while applications for September 2027 for all schools will open early in Autumn 2026. These institutions represent a growing commitment to advanced mathematical education in the UK, encouraging students to push their boundaries and discover the joy of numbers.
