Are you able to clear up it? The numbers all go to 11

It’s two decimal digits lengthy, it’s prime, it’s a palindrome and it’s the variety of gamers in a soccer workforce.

Let’s hear it for “legs” eleven!

At the moment’s puzzles reveal fascinating properties concerning the first quantity past ten.

1. Humorous formation

You’re the coach of a soccer workforce, whose gamers have shirt numbers 1 to 11. The goalkeeper wears 1. You should divide the others into defenders, midfielders and forwards.

You wish to prepare your workforce in order that the sum of the shirt numbers in every group (defenders, midfielders, forwards) is divisible by 11?

Give an instance, or show it isn’t doable.

2. Friends or not

Once we first study our occasions tables, the 11-times desk feels delightfully easy:

11 × 1 = 11
11 × 2 = 22
11 × 3 = 33
…
11 × 9 = 99

All of the solutions are palindromes (numbers that learn the identical backwards as forwards).

If we supply on, as much as 11 x 99, what number of extra solutions are palindromes?

[Hint. At least one! For example, 11 × 56 = 616.]

3. Large divide

Much less well-known than different divisibility guidelines, there’s a easy technique to check for divisibility by 11.

Take the digits of a quantity and add them alternately with plus and minus indicators (beginning with a plus). If the result’s a a number of of 11 (together with 0), then the unique quantity is divisible by 11.

For instance, for 132 we get 1-3+2 = 0, so 132 is divisible by 11.

Utilizing every of the digits 0–9 precisely as soon as, make the biggest doable 10-digit quantity that’s divisible by 11.

I’ll be again at 5pm UK with the options.

PLEASE NO SPOILERS (Focus on your favorite elevens.)

The motivation for in the present day’s puzzles is that eleven can be the variety of College Maths Colleges within the UK. These revolutionary colleges, every hooked up to a college, are state state sixth types for 16–19 yr olds who love maths. College students examine a specialist curriculum designed for many who need to push themselves additional than a normal maths course permits.

There are at present 9 colleges open: King’s and Imperial in London, Exeter, Liverpool, Lancaster, Cambridge, Leeds and Aston. Colleges at Durham and Nottingham got the go-ahead in December, and can open within the coming years.

At College Maths Colleges, playful mathematical engagement like in the present day’s puzzles takes place day-after-day. Purposes for September 2026 are nonetheless open for Exeter, Liverpool, Lancaster, Leeds, Surrey and Aston. Purposes for September 2027 for all colleges open early in Autumn 2026.

Because of the Univsersity Maths Colleges. To search out out extra about their web site is umaths.ac.uk.