Problem 24 · 2024 Math Kangaroo
Stretch
Logic & Word Problems
spatial-reasoningcasework
There are three identical dice on a table (see picture). What is the sum of the three numbers on the bottoms of the dice, touching the table?
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Answer: C — 43
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Hint 1 of 3
All three dice are the same, so a number you can see on one die helps you figure out the other dice too.
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Hint 2 of 3
Two numbers that show up on the same die can never be opposite each other; use that to pair up the faces into opposite pairs.
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Hint 3 of 3
The bottom face touching the table is the one opposite the top face, so find each die's top, swap it for its opposite, and add the three.
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Approach: pair up opposite faces from the three views, then add the bottoms
- The dice are identical, so the numbers seen together on the pictures tell you which faces can sit next to each other and which must be opposite.
- Two numbers shown on the same die are not opposite, and matching this up across all three pictures sorts the faces into opposite pairs.
- Each die's table face is opposite its top face, so swap each visible top for its opposite to get the three bottom numbers.
- Adding those three bottom numbers gives 43.
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