## 22: Split the check

Last week, two of my friends and I went to a restaurant and had a lovely meal. We decided to evenly split the check, so we asked the waiter to just combine the totals. However, …

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Last week, two of my friends and I went to a restaurant and had a lovely meal. We decided to evenly split the check, so we asked the waiter to just combine the totals. However, …

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 ****

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 ****

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 ****

Brenda and Sally run in opposite directions on a circular track, starting at diametrically opposite points. They first meet after Brenda has run 100 meters. They next meet after Sally has run 150 meters past their first meeting point. Each girl runs at a constant speed. // What is the length of the track in meters? // (Also, a challenge for all listeners.) // Spiciness: *** out of ****

My perpetually tricky friend told me that while she was walking through town she saw four particularly vibrant houses. There was an auburn one, a brick one, a cherry one, and one the shade of dogwood rose. She wanted me to figure out the order of the houses. She said that the the auburn came before the the brick one while the cherry one came before the dogwood rose, but the cherry and the dogwood rose were not adjacent. I told her that she hadn’t given me enough information, so she just laughed and told me that she could tell me the color of the first one or the color of the last one, but it wouldn’t help if she did either one. // What color was the second house? // Spiciness: *** out of **** // Note: Not having paper makes this one especially difficult. If you give yourself paper, I think you can rate this puzzle as two chili peppers of spiciness instead of three.