You are expecting guests to your birthday party. You know that there will be at most 8 guests, but you don't know how many will actually come. What is the smallest number of pieces you should divide your cake into, so that no matter how many guests come, everyone (including yourself) can be given an equal share? Note that the whole cake must be used and individuals can have more than one part of the cake.
Here is a similar puzzle: Nine gangsters and a gold bar