IBM Ponder This #032 · December 2000

A man leaves his office every day at 5:00, takes the commuter train and arrives at his hometown depot at 6:00. His wife arrives at the depot at 6:00, in their car, and drives him home. This is everyday procedure.

One day, he leaves his office at 4:00 instead of the usual 5:00, neglects to inform his wife, and arrives at the depot at 5:00 instead of 6:00. He decides to walk home. On the way home he meets his wife, who is driving to pick him up at the usual 6:00. He gets in the car, they drive home and arrive 20 minutes earlier than usual.

Question 1: How long, in minutes, did he walk?

Question 2: What unstated assumptions went into your answer to Question 1? What could go wrong?

We won't be posting a list of solvers this month, but we will post some of the submitted answers for Question 2, starting December 8.

Part 1 originally appeared in a Martin Gardner column (which we were unaware of when we printed the puzzle)

Solution

Best opened after a real attempt

To be added.