Enigma 993: If you lose…
13 September 2019
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From New Scientist #2148, 22nd August 1998 [link]
Each year the four football teams A, B, C and D play each other once, getting 3 points for a win and 1 for a draw. At the end of the year the teams are ordered by total points and those with equal points by goal difference. Any still not ordered are then ordered by goals scored and then, if necessary, by the result of the match between the two to be ordered. Any still not ordered draw lots. The top two teams with a prize.
The order the games are played in can vary, except that A always plays its opponents in the order B, C, D, and A vs B is always the very first match of the year.
By an amazing coincidence the following has happened in 1996, 1997 and 1998. One hour before A v C kicks off, team A’s manager/mathematician announces to the team that if they lose to C then they cannot possibly get a prize. Team A has gone on to win a prize in spite of losing to D.
1. Is it possible in 1996 A vs C was the 3rd game of the tournament?
2. In 1997, A vs C was the 4th games of the tournament. Name the two teams that you can say for certain met in the 2nd or 3rd game of the tournament.
3. In 1998, a total of 4 goals was scored in the tournament. What was the score in B vs C?