1 Aug 2013

Extended Domino Triangles: Upper Secondary Mathematics Competition Question


This is an extension to the previous domino triangles problem; I hope Chris Breederveld doesn’t mind me messing with his puzzle!

In this case, take a full set of dominoes but don’t remove the tiles with blanks. The tiles with blanks can still be used to denote a zero. For example, the tile [2/0] can be used as the fraction 0/2 but obviously not as 2/0! This means that the tile [0/0] is the only one that must be removed as it is effectively useless.

Now the question is essentially the same as before. Starting with the tile [6/6] at the top of the triangle, every tile-fraction is the sum of the two tile-fractions below it. How many unique solutions can you find? Treat reflections as one distinct solution.

The diagram below shows the start of one possible solution. Compare this with the diagram in the previous question.




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