Enigma 974: Girls jump first
7 February 2020
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From New Scientist #2129, 11th April 1998 [link]
Each pony club competing at the gymkhana entered one boy and one girl for the showjumping. In order to determine the order of competition, Mary put all the riders’ names in a hat and drew them out one at a time.
When Mary had drawn precisely half of the names she was surprised to find she had drawn one rider from each club. She calculated that if she did such a draw a thousand times this would only be likely to happen with this number of competing clubs on three occasions (to the nearest whole number). She then realised in amazement that the riders she had drawn in that first half were all the girls.
1. How many clubs were competing?
2. If the number of clubs competing is still as in question 1, on how many occasions (to the nearest whole number) would Mary be likely to draw all the girls first if she carried out the draw five million times?