Enigma 1268: Scoop!
25 December 2014
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From New Scientist #2424, 6th December 2003 [link]
For a summer job I work in an ice-cream parlour. We sell six-scoop “specials” in which customers can choose one scoop each of six different flavours from our extensive range.
One day, a coach party consisting of a prime number of people came in and they each ordered a six-scoop special. I noticed that if you looked at any pair of flavours from our extensive range, then that pair was in precisely one of the coach party’s specials.
How many flavours are there in our extensive range, and how many of the coach party included vanilla (the most popular of our flavours) in their specials?