TapThe Riddle of the Pyramids

…or The Pharaoh’s Puzzle.

This is a puzzle that was given to me at Christmas because it is known that “I like that sort of thing” and the owner couldn’t solve it! I am not surprised. I am coming to the conclusion that it is not soluble. Not that it has no solution, because I suspect that it does, just that there is no rational way to come up with a solution and doing it randomly would take many lifetimes.

The puzzle contains 100 equilateral triangles each brightly coloured using six basic colours (red, orange, yellow, green, purple and pink). The combination of colours and their pattern around the circumference of each triangle differs from piece to piece. All six colours appear on each piece and except for 18 duplicates, they are each unique.

The object of the puzzle is to use all the 100 pieces and build a large equilateral triangle with a base of 45cms (10 pieces). Other than the colours there are no deliberate distinguishing marks on the pieces so there is no way to tell edges from insides. The interior circles on each piece are identical. So mathematics tells us that there are 100! (100 factorial) different arrangements of pieces – that is about 10 ^ 158 or 1 with 158 zeros following. Clearly some pattern matching reduces this considerably as bad matches are eliminated but using the best algorithm I could come up with and the fastest computer available I could not reduce the time required to solve it to within my lifetime or even this millennium. The only other feature I could extract from the pieces was that there were 20 edges (pairs of colours) that didn’t have a corresponding edge to match up with so must occur on the outside; but which of the occurrences of those edges they actually are is anybody’s guess.

So…do you know this puzzle and do you have a solution or even insight to a better method? If so I would like to hear from you. The publishers, “Brand Makers International Ltd” of Kirby Muxloe seem to be out of business.

[Update] I realise that my description wasn’t good enough as a couple of people have written to say that they didn’t undertstand what the problem was. So I have scanned a few of the pieces so you can see how they have to fit together—colour matching to colour. Do that 100 times and you are done.

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