From New Scientist #2311, 6th October 2001 [link]
To test my nephew’s arithmetic I get him to write down a three-figure number and then to write down the next twenty consecutive numbers as well. Then he has to “reverse” each of the numbers (so that 237 would become 732, and 540 would become 45, and so on). So, for example, if his starting number was 185 then the twenty-one numbers he would get would be: 581, 681, 781, 881, 981, 91, 191, 291, 391, 491, 591, 691, 791, 891, 991, 2, 102, 202, 302, 402 and 502.
I then ask him to cross out all those numbers which are divisible by 2, then from what’s left to cross out all those numbers divisible by 3, then from what’s left to cross out all those numbers divisible by 5, then from what’s left to cross out all those numbers divisible by 7, and finally from what’s left to cross out all those numbers divisible by 11. So, for example, if he started with 185 (as above) then he would end up with just the six numbers 881, 191, 391, 491, 691 and 991.
On one occasion recently he chose his three-figure starting number, carried out the above process and when he had finished he was left with 14 numbers. By some neat logic you can work out what the starting number was.
What was it?