Dice Corner
You’re looking through a hole at the corner of a standard die. The image below shows all you can see through the hole: portions of three faces meeting at the corner.
What number appears on one of these three visible faces? You do not have to identify the exact face it is on.
A property about dice
On a standard die, opposite faces sum to 7. At any corner, the three visible faces include one from each opposite pair: (1, 6), (2, 5), and (3, 4).
Solution
6.
On a standard die, opposite faces sum to 7: the pairs are (1, 6), (2, 5), and (3, 4). At any corner, the three visible faces include exactly one face from each pair.
The 1 has a single pip in the centre of the face — far from any corner. If the 1 were visible, its corner would show no pips through the hole. But all three corners show a pip.
Since the (1, 6) pair must contribute one face, and it can’t be the 1, the visible face must be the 6.
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