Problem 8 · 2016 Math Kangaroo
Medium
Counting & Probability
casework
I have some unusual dice. On their faces are the digits 1 to 6 as usual, however the odd numbers are negative (so −1, −3, −5 instead of 1, 3, 5). I throw two such dice at the same time. Which of the following sums can I definitely not achieve with one such throw?
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Answer: D — 7
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Hint 1 of 2
List the six face values: −1, 2, −3, 4, −5, 6.
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Hint 2 of 2
Try to write each target as a sum of two of those values.
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Approach: reachable sums
- Each die shows one of −5, −3, −1, 2, 4, 6.
- Sums 3, 4, 5, 8 are all possible (e.g. −1+4, 2+2, −1+6, 2+6).
- No pair adds to 7, so 7 cannot be achieved.
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