My neighbor has nine kids (all under 21), and their ages are such that you can never pick three kids so that the middle one is the average of the ages of the extreme ones. What are their ages?
(Note that you could also say that you can never find three kids whose ages are in arithmetic progression.)
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Submitted by e.g.
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Rating: 4.1250 (8 votes)
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Solution:
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(Hide)
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The basic solution, with all ages between 1 and 20, is 1, 2, 6, 7, 9, 14, 15, 18, 20. Replacing all ages with their difference to 21 also works (20, 19, 15, 14, 12, 7, 6, 3, 1) but is essentially the same solution. If you allow kids to be 0 years old (babies?) then there are many more solutions, as Penny showed. |
