Problem 20 · 2015 Math Kangaroo
Hard
Spatial & Visual Reasoning
dice-faces
On a standard die the sum of the numbers on opposite faces is always 7. Two identical standard dice are shown in the figure. How many dots could there be on the non-visible right-hand face (marked with “?”)?
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Answer: A — only 5
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Hint 1 of 2
The two dice are identical, so they have the same handedness: the cyclic order of the 1-2-3 corner is the same on both.
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Hint 2 of 2
Read the top and front pips of the right die, then use that fixed handedness to read off the third (right-hand) face.
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Approach: use the matching handedness of two identical dice
- From the left die you can read the way its 1, 2 and 3 faces turn around their shared corner; the right die, being identical, turns the same way.
- On the right die the top and front faces are shown, so its handedness fixes the remaining (right-hand) face to a single value.
- That forces the marked face to be exactly 5 (A).
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