CAFE CHALLENGE: well-behaved numbers

This is for one of those Coffee Shop moments?

You know, the time when you just want to stop, rest and grab a coffee – but know you need to keep the children focused on something more meaningful than mobile phone game.

Well, here’s a solution: A Quick Cafe Challenge


Well-behaved Numbers

Think about the date your birthday falls on. Write the number in words. Do any of the letters repeat? The chances are they do.

I was born on the 27th, and TWENTY-SEVEN is a terribly greedy number. Look at all those E’s! There are two T’s and two N’s as well.

Some numbers are better behaved. Think about the number TEN, it doesn’t repeat any letters.

Another ‘well-behaved number is EIGHT.

Then we meet NINE who insists on repeating those ‘N’s.

ELEVEN is even worse, using up three E’s.

I’m going to call numbers, like 10 and 8 (who don’t repeat any letters), Well Behaved Numbers.


Now, here’s the challenge:

How many Well-behaved Numbers can you find?

Go on, grab a bit of paper and a pencil… you have ten minutes.



You might think there are a lot of them, but there are only 15 Well Behaved Numbers above zero. If you include zero itself then there are 16 (That’s another hint).

One further clue may also help: only one of the numbers is greater than 100.




Here are the 16 Well-behaved Numbers. These are the only ones, out of an infinite set of numbers!

0, 1, 2, 4,

5, 6, 8, 10,

40, 46, 60, 61,

64, 80, 84, 5,000

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