This problem is dedicated to the stalwart and skilled Macalester men's soccer team. They were robbed!
Alice: Did you hear about the penalty kick shootout between the WorthWit and MacScot soccer teams?
Bob: I heard only that the MacScots shot first. What was the score? Who won?
Alice: The score was interesting. If I told you the score, you could tell me who won.
Notes: A penalty kick shootout in soccer works as follows: There are five rounds of the form: Team A shoots; then team B shoots. However, if at any point the score is such that a team is guaranteed to win, the shootout ends. If they are tied after five rounds, then additional rounds are played until there is a winner. A score is reported as m-to-n where m > n (regardless of who shot first).
You also need to know that PKs come as a round of 5, with shots in the order ABABABABAB, but coming to a stop once one of the teams is a guaranteed winner. So a score such as 5-0 is not possible.
Postscript: writing down who has to know what for this to work,
Alice has to be smart (so that any computations she does are correct.)
You have to know that Alice is smart.
Alice has to know that Bob is smart, since she makes a statement about what Bob can do.
Therefore Bob has to be smart.
* Last Friday there was a very exciting NCAA Div. III soccer playoff game at Macalester. Whitworth C. scored in the 26th minute. Macalester equalized with 3 minutes left in the game. Nothing happened in overtime, so it went to a penalty kick shootout. Whitworth prevailed, after a controversial call by a linesman about the keeper's movement.
© Copyright 2001 Stan Wagon. Reproduced with