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Problem of the Week 947

Who Won?

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.

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 permission.


14 November 2001