In a playful nod to the iconic "Spinal Tap" amplifier that famously goes up to eleven, today's mathematical journey delves into the fascinating properties of the first number beyond ten. Eleven is not just a prime palindrome or the number of players in a football team; it's a source of delightful puzzles that challenge logic and creativity.
Funny Formation: A Football Coach's Conundrum
Imagine you are the coach of a football team where players wear shirt numbers from 1 to 11, with the goalkeeper in number 1. Your task is to divide the remaining ten players into three groups: defenders, midfielders, and forwards. The twist? You must arrange the team so that the sum of the shirt numbers in each group is divisible by 11.
Is this possible, or is it a mathematical impossibility? This puzzle invites you to either provide a valid example or prove that no such arrangement exists, testing your strategic thinking and numerical skills.
Pals or Not: Exploring the 11-Times Table
Many of us recall the simplicity of the 11-times table from early school days, where results like 11, 22, and 99 are palindromes—numbers that read the same forwards and backwards. But what happens when we extend this beyond the basic range?
If we calculate 11 multiplied by numbers up to 99, how many of these products remain palindromic? For instance, 11 × 56 equals 616, a palindrome. This puzzle encourages you to count the additional palindromes beyond the familiar first nine, delving into patterns and number theory.
Big Divide: Mastering Divisibility by 11
Less known than other divisibility rules, there's 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 result is a multiple of 11 (including zero), the original number is divisible by 11.
For example, with 132, we compute 1 - 3 + 2 = 0, confirming divisibility. Your challenge is to use each digit from 0 to 9 exactly once to create the largest possible 10-digit number that passes this test. This puzzle combines combinatorial thinking with arithmetic precision.
Inspired by Innovation: UK University Maths Schools
The motivation behind these puzzles stems from the eleven University Maths Schools across 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 push students beyond standard courses, fostering deep engagement with the subject.
Currently, nine schools are operational, including King's and Imperial in London, Exeter, Liverpool, Lancaster, Cambridge, Leeds, and Aston. Durham and Nottingham have received approval and will open in the coming years, expanding this educational network.
At these institutions, playful mathematical exploration, much like today's puzzles, is a daily occurrence. Applications for September 2026 are open for Exeter, Liverpool, Lancaster, Leeds, Surrey, and Aston, with applications for September 2027 opening in early Autumn 2026.
Remember, no spoilers! Feel free to discuss your favourite elevens or mathematical insights as we await the solutions later today.
