FILE No.68Unsolved
A die at a gambling den was swapped for a rigged one. Police studied photographs of four dice. Each photo shows the three faces visible from one corner.
On a normal die, opposite faces always add up to 7: 1 is opposite 6, 2 opposite 5, 3 opposite 4.
The three faces seen from one corner are all next to each other.
Which die shows an impossible combination?
If you get stuck, open the hints one at a time, in order.
What do opposite faces add up to?
Can opposite faces be seen from the same corner?
Look for a pair that adds to 7.
Which die shows an impossible combination?
Choose the answer closest to the truth.
Die C (1, 4, 6)
The answer is: Die C (1, 4, 6).
Faces visible from one corner are mutually adjacent, so none of them can be opposite another. On Die C, 1 and 6 add up to 7, so they are opposite faces and cannot be seen together.
Dice A, B and D have no pair adding to 7 (for B: 2+3=5, 2+6=8, 3+6=9; for D: 4+5=9, 4+6=10, 5+6=11), so they are possible.
A set like 1, 4, 6 looks like a random, perfectly ordinary mix of numbers.
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