**From New Scientist #1321, 2nd September 1982** [link]

Our local tennis club has just had its annual knockout tournaments. All the male members played in the men’s singles, and all the female members played in the women’s singles. Luckily there was an even number of men and so they were able to form pairs and all take part in the men’s doubles. Similarly, all the ladies took part in the women’s doubles. The men and women paired off as far as possible for the mixed doubles, but some women had to miss this even because of a shortage of men. The total number of matches in all five competitions was just 11 more than the total number of byes necessary in all five competitions (some being necessary in each), and this total number of byes was 100 more than the total number of members in the club.

How many women and how many men in the club?

[enigma176]

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I assumed that the knockout tournament was a “single-elimination” tournament [ http://en.wikipedia.org/wiki/Single-elimination_tournament ]. The fun here was writing a neat function to determine the number of byes. I wrote a recursive function, so that it can be cached using the

cached()function fromenigma.py, which is fine for the relatively small number of participants in a tennis tournament. This Python code runs in 36ms.Solution:There are 130 women and 34 men in the club.