The October 2007 Using your Head is Permitted riddle,
one of the first riddles ever published on this website, is a
question about jigsaw puzzles.
Briefly, it asks the following question: if I am trying to solve an
To make this question more concrete, the following model was offered: the
puzzle contains a known set of We assume that the connectivity graph has no self-symmetries, meaning that if one was to compare every pair of tiles to see if they are to be mapped to neighbouring positions on the connectivity graph, one will have excluded by this all possible assignments of tiles to positions, except for the one true solution to the puzzle. Define the "difficulty" of a puzzle to be the minimum number of pairs of tiles that one must try to match together in this puzzle before one is sure to have narrowed down the list of possible assignments to only the one true solution. By "minimum" we mean that one employs the best possible strategy for the given graph, and by "sure" we mean that one must take into account the worst possible sequence of outcomes to the tile-match operations.
Define the difficulty of a
The question was: let This month's riddle:
Solve this riddle again, only this time, do not restrict yourself to sets of
puzzles with a bounded All answers should come with proofs, as usual. Solvers are welcomed to check out the answer to the original riddle. |
## List of solvers:Dorian Nogneng (9 July 14:55)Jin Ruizhang (11 July 03:49) |

Elegant and original solutions can be submitted to the puzzlemaster at __riddlesbrand.scso.com__.
Names of solvers will be posted on this page. Notify if you don't want
your name to be mentioned.

The solution will be published at the end of the month.

Enjoy!