by Andrew Skidmore
Published Friday May 03 2024
In our darts league, each team plays each other once. The result of each match is decided by the number of legs won, and each match involves the same number of legs. If both teams win the same number of legs, the match is drawn. The final league table shows the games won, drawn or lost, and the number of legs won for and against the team. The Dog suffered the most humiliating defeat, winning only one leg of that match. Curiously, no two matches had the same score.
What was the score in the match between The Crown and The Eagle?
Sunday Times Teasers Discussion Group 
There is a short analytical route to the answer – if you find it. I started off in the right direction, then missed a key inference and roamed in the wilderness. When I went back I found the missed step, and the answer was soon apparent. There was an interesting twist at the end.
This teaser is a variation on the football league teasers which used to to be much more common. They are not to everybody’s liking. I enjoy the challenge of finding logical solutions. This teaser is well constructed.
I wrote down possibilities for the four numbers of winning legs for all the matches of one team, along with the team played if known. I then added consistent numbers in each case for a second team, then third, fourth, fifth. Along the way I added which team was played when known and eliminated cases that did not work within the conditions of the question.
With careful choice of which order to take the teams in, the problem is not as big as it sounds.
I did end up with more than one possible outcome, but the score for C vs E is the same in each case.
The key for me was knowing some scores (from the Draw) and working out which team was the only possible one to give Dog only one point.
Nice exercise in logic through series of “what-if” considerations. My final conclusions left scores in 4 matches undefined but if the winner of any of these 4 were known it would allow all match scores and winners to be uniquely defined. Happily, match C vs E is not one of these 4.
My revised solution requires four lines to reach the answer. There is only one possible set of legs won by A and B together. Then there is only one possible set for C and E together. The answer follows directly. It is only necessary to know the scores in two matches: AvB and CvE.