# The Grey Labyrinth is a collection of puzzles, riddles, mind games, paradoxes and other intellectually challenging diversions. Related topics: puzzle games, logic puzzles, lateral thinking puzzles, philosophy, mind benders, brain teasers, word problems, conundrums, 3d puzzles, spatial reasoning, intelligence tests, mathematical diversions, paradoxes, physics problems, reasoning, math, science.

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bonanova
Daedalian Member

 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 Cos(x) = answer. I wonder if there are other problems like this, or if there is a prototypical problem that this analysis describes that can be flavored to generate a family of seemingly different problems. Or does that question even make sense?_________________ Vidi, vici, veni.
L'lanmal
Daedalian Member

 Posted: Sat Mar 09, 2013 6:21 pm    Post subject: 2 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).
Nsof
Daedalian Member

 Posted: Sun Mar 10, 2013 8:27 pm    Post subject: 3 Fibonacci numbers creep up in many puzzles/problems._________________Will sell this place for beer
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