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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