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Programming Enigma Puzzles

6 June 2015

Posted by on **From New Scientist #1433, 6th December 1984** [link]

The diagram shows all the draws in the recent Golden Rook all-against-all chess tournament. In all other games, the winner scored 1 and the loser 0. Play was in five rounds with three games each.

“How did you do?”, I asked Alexander Alapin.

“Not well”, he replied. “Freddie French and I were so worn out by our first round draw (with each other) that we came equal bottom behind all the rest”.

“A lot of draws!”, I remarked.

“Yes. At least one in each round, with each player drawing in at least two consecutive rounds”.

There were two equal winners. Given that they did not meet in the second round, can you work out who they were and whom they played in the final round?

[enigma286]

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This Python3 program runs in 83ms.

Solution:The winning players were Colle and Dragon. In the final round Colle played French and Dragon played Bishop.There is only one possible sequence of rounds, but there are three possible outcomes for the matches (distinguished by the numbers in square brackets below):

Round 1: AvF (draw), BvE (draw), CvD (C wins [1, 2], D wins [3])

Round 2: AvB (draw), CvE (C wins [1, 3], E wins [2]), DvF (draw)

Round 3: AvC (A wins [1], C wins [2, 3]), BvF (B wins), DvE (draw)

Round 4: AvD (D wins [1, 2], A wins [3]), BvC (draw), EvF (draw)

Round 5: AvE (E wins [1, 3], A wins[2]), BvD (D wins), CvF (draw)

The final scores are always: C and D, 3 points; B and E 2½ points; A and F, 2 points.