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 [quote="Nsof"]Fibonacci numbers creep up in many puzzles/problems.[/quote]
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Nsof
Posted: Sun Mar 10, 2013 8:27 pm    Post subject: 1

Fibonacci numbers creep up in many puzzles/problems.
L'lanmal
Posted: Sat Mar 09, 2013 6:21 pm    Post subject: 0

If you are looking for a family of puzzles which all have the same equation as an answer (and not just the particular equation you described), you might want to check out exercise 6.19 of Stanley's Enumerative Combinatorics. The exercise is to prove that 66 different sets are all counted by the same formula (namely: the Catalan numbers).
bonanova
Posted: Sat Mar 02, 2013 10:32 am    Post subject: -1

I notice that two disparate problems can be solved by the same equations. The chestnut about adding 1 foot to the length of a tight band around the equator and raising the band with a pole as high as possible at one point is one; the optimal escape path for the girl rowing a boat in a circular lake (recently posted here) is another.

Eventually you get the equation

Tan(x) = x + c

where c is some value you can calculate. You need x because the answer to the problem is