Enigma 161: Two times table
14 January 2014
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From New Scientist #1306, 20th May 1982 [link]
Lunchtime at Bramfield School is currently being taken up with a five-a-side soccer competition, in which five teams are playing in a league and will eventually play each other just once. Young James, who has shown himself to be more capable of tackling sums than footballers, is keeping a record of the results from the touchline, and has the table below as his latest check:
It is surprising, even with James’s keen eye for numbers, that he has spotted that the sum of all the numbers in this table is twice what it was earlier in the competition (when the league had no clear leader[*]).
What had been the results at that stage?
[*] This phrase is intended to imply two or more teams had the same number of points at the top.
I don’t think there is a unique solution to this puzzle (as the problem statement implies).