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- Some marbles in a bag are red and the rest are blue. If one red marble is removed, then one seventh of the remaining marbles are red. If two blue marbles are removed instead of one red, then one-fifth of the remaining marbles are red. How many marbles were in the bag originally?
- A list of 8 numbers is formed by beginning with two given numbers. Each new number in the list is the product of the two previous numbers. Find the first number if the last three are shown:
______, ______, ______, ______, ______, 16, 64, 1024
- There are 120 seats in a row. What is the fewest number of seats that must be occupied so the next person to be seated must sit next to someone?
- Starting with a regular hexagon, a smaller hexagon is made by connecting the midpoints of its sides. How much of the area of the large hexagon does the smaller one take up?
- You are standing on a square of an infinite checkerboard. You can move from any square to any adjacent square (no diagonals). How many squares are exactly ten moves away? (That is, the squares that can be reached in ten moves, but not in any fewer.
- The Cube Game is played by two players. The players start at opposite corners of a cube. Instead of taking turns, the players move at the same time. Each player moves from his current position to any adjacent corner. The game ends when both players move to the same corner. What is the length of the shortest possible game?
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