## Brain-Teaser 497

**From The Sunday Times, 6th December 1970** [link]

All 26 members of the Alphabets Cricket Club (all surnames starting with a different letter of the alphabet) turned up for the annual general meeting at the Ugly Duck. Afterwards they divided into 5 teams of 5 and played a quick game of skittles, the lowest-scoring team to buy beer for the rest. (P. L. Zeigler sportingly stood down).

Each player had just one ball at the 9 skittles, scoring, of course, a point for each skittle knocked down. The team captains varied in performance: Thomson got 9, Knight 5, Oldwhistle 3, C. F. Arrowroot 2, and the luckless Fisher 0. (Fisher’s team moved to have all captains’ scores ignored, but the plea was rejected; it was pointed out that anyhow Fisher’s weren’t due to buy the beer).

The team totals were all different, as indeed they would have been had captains’ scores been ignored. No other player made the same score as any Captain, and no two team members of the same team made the same score. Oldwhistle’s team won.

What was the order of finishing, and what were the individual scores of the team buying the beer?

[teaser497]

## Jim Randell 9:50 am

on3 September 2019 Permalink |This Python program considers the set of scores for the winning team, and then looks for possible scores for the remaining teams that gives the teams different scores (both including and excluding the captains scores).

Run:[ @repl.it ]Solution:The finishing order was: 1st = Oldwhistle, 2nd = Thomson, 3rd = Knight, 4th = Fisher, 5th = Arrowroot. The individual scores of the team buying the beer were: 1, 2 (Arrowroot), 4, 6, 8.The complete set of results is:

There is also a “near miss” solution:

But this is disallowed as team F is last (and wouldn’t be last if the captains scores are ignored).

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