**From New Scientist #2272, 6th January 2001** [link]

Albion, Borough, City, Rangers and United played a tournament in which each team played each of the other teams once. Two matches took place in each of five weeks, each team having one week without a match.

One point was awarded for winning in the first week, 2 points for winning in the second week, 3 points for winning in the third week, 4 points for winning in the fourth week and 5 points for winning in the fifth week. For a drawn match each team gained half the points it would have gained for winning it. At any stage, teams that had gained the same number of points were regarded as tying.

After the first week A led, with B tying for second place. After the second week B led, with C tying for second place. After the third week C led, with R tying for second place. After the fourth week R led, with U tying for second place. After the fifth week U had won the tournament with more points than any of the other teams.

(1) Which team or teams finished in second place after the fifth week?

(2) Give the results of Albion’s matches, listing them in the order in which they were played and naming the opponents in each match.

This completes the archive of *Enigma* puzzles from 2001. There are now 1065 *Enigma* puzzles on the site, the archive is complete from the beginning of *Enigma* in February 1979 to January 1987, and from January 2001 to the final *Enigma* puzzle in December 2013. Altogether there are currently 59.5% of all *Enigmas* published available on the site, which leaves 726 *Enigmas* between 1987 and 2000 left to publish.

[enigma1116]

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This Python 3 program attacks the problem recursively. Internally it deals in half-points, so that the totals remain integers. It runs in 76ms.

Solution:(1) Albion finished in second place; (2) Albion’s matches were: week 1 = beat City, week 2 = lost to Borough; week 3 = no match; week 4 = drew with United; week 5 = beat Rangers.The complete results are: