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Telly's calendar (Posted on 2013-08-06) Difficulty: 2 of 5
Telly Monster is a friend of mine who loves triangles (and puzzles). He has asked me to make him a wooden calendar using triangles for the months. Can you design 9 wooden triangles with a letter in each corner that when rotated or rearranged will spell out all of the months of the year.

For example:

/? ?\ /? ?\ /? ?\ /? ?\ 

See The Solution Submitted by jduval    
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re: Computer aided - all solutions. | Comment 4 of 5 |
(In reply to Computer aided - all solutions. by jduval)

writing a program to solve this was and is daunting. Consider that,starting with SEPTEMBER as a given for a list of necessary letters spread across all 9 triangles, the remaining lettters are OOUUAADCVJYGFNRHIL. There are 18! / 2^3 ways of arranging these. If we do it recursively with one letter at each level of revursion, we can prune the tree further by not placing a third letter on a given triangle unless it's later in the alphabet than the second letter placed on that triangle,but that still leaves 18! / 2^12 = 1.56... * 10^12 arrangements needing evaluation.

An alternative would be to do months successively instead of letters in arbitrary order, but this would entail ordering of possible placements of lettters within a month. It seemed an seems simpler to do the puzzle manually.
  Posted by Charlie on 2013-09-23 12:26:21

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