Legs eleven, Ocean’s Eleven, elevenses!

Yes, let’s hear it for the number 11, star protagonist of today’s puzzles.

Eleven is the first number you reach once you go beyond ten. Since ten is the base of our number system, eleven’s position gives it some interesting properties – as the members of Spinal Tap knew all too well.

(Although you might need to turn up your brains to 11 and a half for today’s puzzles.)

The first one concerns palindromic numbers – that’s those numbers that read the same forwards and backwards, such as 121 or 556655.

*1) Show that every even-digit palindromic number is divisible by 11.*

(An even-digit palindromic number is a palindromic number that contains an even number of digits, like 1221, or 678876.)

*2) More than 100 people live in a village. Prove there are 11 people living in the village for whom the sum of their ages is divisible by 11.*

I’ll be back with the answers at 5pm UK time.

Meanwhile, NO SPOILERS! Instead please reminisce about Spinal Tap, list your favourite wearers of the 11 shirt, or select your favourite mathematical anecdote about the number 11.

I’m hoping this column is the start of an occasional series devoted to specific numbers. If you have any favourite number puzzles, please let me know!

*I’m the author of several books of popular maths, including the puzzle book Can You Solve My Problems?, as well as the Football School book series for kids that explains the world through football.*

*I set a puzzle here every two weeks on a Monday. I’m always on the look-out for great puzzles. If you would like to suggest one, email me.*

*Sources for today’s puzzles*

*1) Suggested by Angayar Pavanasam, of the National Institute of Technology, Trichy, India.*

*2) Adapted from Half A Century of Pythagoras Magazine, edited by Alex van den Brandhof, Jan Guichelaar and Arnout Jaspers.*