Domino Puzzle: Lower Secondary Mathematics Competition Question

You are given a full domino set of 28 tiles. Firstly, remove all the tiles that have a blank end, leaving you with 21 tiles. Now, by looking at each tile as a vertical arrangement of numbers, we are going to use them as fractions. For example, the tile [5,2] can be thought of as the fraction 5/2 or 2/5.

Your task is to find all the combinations of 5 distinct tiles such that the product of 4 of the fractions is equal to the 5th fraction, which is itself equal to the number 3.

Algebraically, this equates to:

where the square brackets [A/B] merely serve as a reminder that these are domino tiles. The order of the 4 tiles on the left-hand side is not important.

Short Question

Find all the solutions where the above product equals 3 and that include the tile [5/2].

Project Question

Find all the solutions where the above product equals 3.

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