30 Jul 2013

Domino Triangles: Winner of PMQ20: Middle Secondary Mathematics


Before launching into the question itself, note that this question was the winner of PMQ20, where you were asked to design your own question based around dominoes. A big “Thank You” to Chris Breederveld for submitting the puzzle below.

The Question

Take one full set of dominoes and remove those tiles with blanks, leaving you with 21 distinct tiles. Orient each tile vertically so that it denotes a rational number. For example, the tile [5/2] can be used as the fraction 5/2 or as 2/5. The aim is to arrange six tiles into a triangular grid in such a way that a tile-fraction is the sum of the two tile-fractions immediately below it.

Given that the tile at the top of the triangle is [6/6], how many solutions can you find? Treat reflections as one unique solution.

The diagram below shows the start of one possible solution. Note that the only restriction is that the [6/6] must be at the top.






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