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:

-/J\---/U\---/L\---/Y\- 
/? ?\ /? ?\ /? ?\ /? ?\ 

(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