**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?

[enigma1470]

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Assuming “a run of five sequential numbers” means “five consecutive integers” (in either ascending or descending order). The following Python program finds two different solutions in 42ms.

Solution:The opposite pairs of numbers on the die moved by Isabella are: 1 and 4; 2 and 6; 3 and 5.