Problem 19 · 2020 Math Kangaroo
Hard
Spatial & Visual Reasoning
dice-facespath-tracing
The points on opposite sides of an ordinary die add up to 7. This die is placed on the first square as shown and then rolled along, as in the picture, to the fifth square. When the die reaches the last square, what is the product of the numbers of points on its two coloured vertical faces?
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Answer: D — 18
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Hint 1 of 3
The two side faces are partners that always add to 7, so once you know one, you know the other.
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Hint 2 of 3
Roll a real die (or imagine one) tipping forward square by square and watch the side faces.
Still stuck? Show hint 3 →
Hint 3 of 3
Only the forward tips change the top and front faces; the two side numbers stay as a pair the whole way.
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Approach: roll the die step by step and read the two colored side faces at the end
- Set a real die the same way as the picture and tip it forward, one square at a time, following the arrows to the last square.
- Keep checking the two colored side faces, remembering that whatever shows on one side, its hidden partner is 7 minus that number.
- On the last square the two colored side faces show 3 and 6, and 3 × 6 = 18, choice D.
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