Domination Puzzles
An original set of puzzles that use a standard set of 28 dominoes.
Email your answers to andy.brown@puzzlemanic.com, there may be a prize for the best set of solutions received! Answer key: the value requested for each question plus for each row/layer from top to bottom list the half-dominoes or dominoes in order from left to right using a hyphen to indicate an empty space (eg 46 - 5 - 36).
Domination Puzzle Number 1
Domination Puzzle Number 2
Domination Puzzle Number 3
Arrange a standard set of 28 dominoes so that the 8 half-dominoes of each type (0-6) appear in two squares of 4 adjacent half-dominoes each and the total number of half-domino edges not touching another domino is a minimum.What is the minimum number of non-touching half-domino edges?
eg an arrangement for only 6 dominoes (12 half-dominoes) 2-2 2-1 2-0 1-1 1-0 0-0, containing three squares of 4 adjacent half-dominoes (which has 16 non-touching half-domino edges) is:
Arrange a standard set of 28 dominoes in a stack so that every half-domino (0-6) can only be covered by the same type of half-domino, all half-dominoes must be directly supported by the next layer down and the number of half-dominoes on the bottom layer of the domino stack is a minimum. What is the number of half-dominoes on the bottom layer of the domino stack?
eg an arrangement for only 10 dominoes 0-0 0-1 0-2 0-3 0-4 1-1 1-2 1-3 1-4 2-3, containing three layers of dominoes (which has a base layer containing 8 half-dominoes) is:
Arrange a standard set of 28 dominoes in a stack so that for each domino at least one of it's half-dominoes (0-6) is covered by the same number of half-dominoes as the sum of pips on the domino in question, all half-dominoes must be directly supported by the next layer down and the number of half-dominoes on the bottom layer of the domino stack is a minimum. What is the number of half-dominoes on the bottom layer of the domino stack (or if it is not possible to create a complete stack what is the maximum number of dominoes it is possible to stack so that these conditions hold)?
eg an arrangement for only 8 dominoes 0-0 0-1 0-2 0-3 0-4 1-1 1-2 1-3, containing five layers of dominoes (which has a base layer containing 4 half-dominoes) is:
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