This one is actually quite simple once you see it. Consider the following converation between man 1 and man 2: Man 1: 'I have a puzzle for you. First, pick an integer from 100 to 999 in your head.' Man 2: 'Uuhhm. Well.. okay. (thinks: I`ll take 501, 'cuz that me lucky number.') Man 1: 'Okay, consider the number that you get by repeating the number in your head once. So if you had 123, you should have 123123.' Man 2: 'Okay. (That'll be 501501)' Man 1: 'Now divide that number by 13.' Man 2: '..wait a sec.... okay. Fortunately it's an integer. (that's 38577)' Man 1: 'Divide that number you got by 7' Man 2: '..(that'll be 5511).. okay. Luckily another integer!' Man 1: 'Now divide it by 11.' Man 2: '(5511/11 is..eh 501). Hey, I get the number with which I started.' Man 1: 'Really? I suppose you made a good choice at the start. My question is: How many integers from 100 to 999 have this property?' So, how many integers are there from 100 to 999 which have this property?