Enigma 1470: Dicey dice
25 January 2013
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From New Scientist #2631, 24th November 2007
Isabelle has a set of five dice each of which has faces showing different numbers from 1 to 6. Among them, no two pairs of opposite faces are the same, and the die with 2 opposite 4 does not have 3 opposite 6.
When her brother George recently stacked them in a single four-sided vertical column, Isabelle noticed that one side showed a run of five sequential numbers.
George then carefully moved the bottom die, without changing its orientation, to the top and Isabelle saw that the same sequence now appeared along one of the other sides.
Isabelle then tried the same move herself with a second die and George a third, and each time the original sequence was created on another side.
What pairs of opposite numbers appear on the die moved by Isabelle?