Cornelius got a flat tire on a miserable, rainy day. As he was changing it on the side of the road, he placed the four lug nuts in the overturned hub cap. As our dear friend was moving back to put on the spare, he accidentally bumped the hub cap. He watched helplessly as all four lug nuts rolled into a deep sewer and were whisked away. Then our friend had a brilliant solution and within minutes was driving safely away.

What was his solution?

At a party of thirty-five people there are twice as many women as children and twice as many children as men. How many of each are there?

You are decorating for spring and you’ve found a bargain. A huge box of beautifully decorated tiles, enough to provide a border in two rooms. You really can’t figure out how to arrange them. If you set a border of two tiles all around, there’s one left over. If you set three tiles all around or four or five or six there’s still one tile left over. Finally you try a block of seven tiles for each corner and you come out even. What is the smallest number of tiles you could have to get this result?