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#221 Logical World Cup

Set by Colin Beveridge

鈥淒rat,鈥� said Ron the reporter. 鈥淣ow the Logical World Cup is over, the editor wants to know how many games each team won, drew and lost, but all I have are the points totals.鈥�

鈥淢aybe I can help,鈥� said Martha the mathematician. 鈥淪how me what
测辞耻鈥檝别&苍产蝉辫;驳辞迟.鈥�

Ron passed her the sheet of paper he had been glaring at.

Solution next week

#220 Artificial Intelli-Vision song contest

Solution

Eight countries took part and the winning song scored 36 points.

If there are N countries, each judging panel gave scores to N-1 songs, and the score of 10 was then deducted, so the 222 total points = (number of countries in the final round 鈥� 2) x the sum of each different number that the panels chose. No countries tied, so there are at most nine different countries. Since the factors of 222 are 2, 3, and 37, there must have been eight scores (from eight countries) that added to 37.

We know one score was 7 points, and the only combination that adds to 37 is 9,7,6,5,4,3,2,1. The best musical act must have scored 37-1 = 36.