## Teaser 2775: Strictly not

**From The Sunday Times, 29th November 2015** [link]

Four celebrities entered a dance competition. Five judges each shared out their eight marks among the four dancers, with each getting a non-zero whole number. Each judge split the eight marks in a different way and then allocated them as follows. Amanda’s marks to Lana and Natasha added to the same total as Barry’s marks to Madge and Paula. Barry gave more marks to Madge than to any other dancer, Charles gave more to Paula than to any other, and Doris gave more to Natasha than to any other. Lana scored more from Edna than from Amanda. All dancers had the same total so the head judge’s scores were used, giving a winner and runner-up.

Who was the head judge, who was the winner and who was the runner-up?

[teaser2775]

## Jim Randell 8:51 am

on9 February 2021 Permalink |Each of the 5 judges gives out 8 points, so 40 points are awarded in total. And there are 4 dancers, and they all receive the same total number of points. So each dancer receives 10 points in total.

Each judge awards a non-zero number of points to each dancer, so the points awarded are between 1 and 5.

I used the [[

`SubstitutedExpression`

]] solver from theenigma.pylibrary to find possible collections of points awarded by the judges, and the scores are then examined to determine which judges scores identify a clear winner and runner up.The following run file executes in 80ms.

Run:[ @repl.it ]Solution:Doris was the head judge. Natasha was the winner. Lana was the runner-up.The scores were allocated as follows (L, M, N, P):

There are only 5 different (unordered) ways to divide a score of 8 between 4 dancers, and only one of them (4, 2, 1, 1) gives a clear 1st and 2nd place.

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## Frits 9:26 pm

on9 February 2021 Permalink |LikeLike