A colleague of mine at work shared this excellent resource with me for interesting and perplexing mathematics problems. The Galileo project looks like it has about 100 interesting mathematics problems for students to do for a variety of different age levels.
How many parents do you have?
How many grand-parents do you have?
How many great grand-parents do you have?
How many great-great-grand-parents do you have?
How many great-great-great-grand-parents do you have?
Wait a minute! Do you see a problem with this?