Three travelers stopped at an inn for supper. The innkeeper could offer only baked potatoes. While the potatoes were baking, the weary travelers fell asleep. Soon, one of them woke up, saw the dish of potatoes and took a third of them without waking up the others. Later the second one woke up, saw the dish, and ate a third of the remaining potatoes. Later the third one did the same. When all three were sleeping once again, the innkeeper cleared the table and found 8 potatoes left. How many potatoes were originally on the table?

. While watching a couple of my students play checkers one day I wondered, just how many squares are on that board? I thought and thought and came up with a number greater than 200! Is that possible? Exactly how many squares are there?