6 hours ago
7
It’s two decimal digits long, it’s prime, it’s a palindrome and it’s the number of players in a football team.
Let’s hear it for “legs” eleven!
Today’s puzzles reveal interesting properties about the first number beyond ten.
1. Funny formation
You are the coach of a football team, whose players have shirt numbers 1 to 11. The goalkeeper wears 1. You must divide the others into defenders, midfielders and forwards.
You would like to arrange your team so that the sum of the shirt numbers in each group (defenders, midfielders, forwards) is divisible by 11?
Give an example, or prove it isn’t possible.
2. Pals or not
When we first learn our times tables, the 11-times table feels delightfully simple:
11 × 1 = 11
11 × 2 = 22
11 × 3 = 33
…
11 × 9 = 99
All the answers are palindromes (numbers that read the same backwards as forwards).
If we carry on, up to 11 x 99, how many more answers are palindromes?
[Hint. At least one! For example, 11 × 56 = 616.]
3. Big divide
Less well known than other divisibility rules, there is a simple way to test for divisibility by 11.
Take the digits of a number and add them alternately with plus and minus signs (starting with a plus). If the result is a multiple of 11 (including 0), then the original number is divisible by 11.
For example, for 132 we get 1-3+2 = 0, so 132 is divisible by 11.
Using each of the digits 0–9 exactly once, make the largest possible 10-digit number that is divisible by 11.
I’ll be back at 5pm UK with the solutions.
PLEASE NO SPOILERS (Discuss your favourite elevens.)
The motivation for today’s puzzles is that eleven is also the number of University Maths Schools in the UK. These innovative schools, each attached to a university, are state state sixth forms for 16–19 year olds who love maths. Students study a specialist curriculum designed for those who want to push themselves further than a standard maths course allows.
There are currently nine schools open: King’s and Imperial in London, Exeter, Liverpool, Lancaster, Cambridge, Leeds and Aston. Schools at Durham and Nottingham were given the go-ahead in December, and will open in the coming years.
At University Maths Schools, playful mathematical engagement like today’s puzzles takes place every day. Applications for September 2026 are still open for Exeter, Liverpool, Lancaster, Surrey and Aston. Applications for September 2027 for all schools open early in Autumn 2026.
Thanks to the Univsersity Maths Schools. To find out more about their website is umaths.ac.uk.
