20: The middle digit [**]

08/28/16 • 2 min

How many three-digit numbers satisfy the property that the middle digit is the average of the first and the last digits? // Spiciness: ** out of ****

How many three-digit numbers satisfy the property that the middle digit is the average of the first and the last digits? // Spiciness: ** out of ****

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19: The token tax [**]

A game is played with tokens according to the following rule. In each round, the player with the most tokens gives one token to each of the other players and also places one token into a discard pile. The game ends when some player runs out of tokens. Players A, B, and C start with 15, 14, and 13 tokens, respectively. // How many rounds will there be in the game? // Spiciness: ** out of ****

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21: The faulty odometer [***]

A faulty car odometer proceeds from digit 3 to digit 5, always skipping the digit 4, regardless of position. For example, after traveling one mile the odometer changed from 000039 to 000050. If the odometer now reads 001729, how many miles has the car actually traveled? // Spiciness: *** out of ****