Problem 10 · 2019 Math Kangaroo
Medium
Algebra & Patterns
sum-constraint
The six smallest odd natural numbers are written on the sides of a die. Toni rolls the die three times and adds the numbers. Which sum will Toni not be able to make?
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Answer: E — 35
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Hint 1 of 3
The six smallest odd numbers are 1, 3, 5, 7, 9, 11, so those are the faces.
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Hint 2 of 3
Adding three odd numbers always gives an odd result, and there is a biggest total you can ever reach.
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Hint 3 of 3
Find that biggest possible total and check each answer against it.
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Approach: bound the achievable totals
- The faces are the odd numbers 1, 3, 5, 7, 9, 11, and the biggest total you can roll is 11 + 11 + 11 = 33.
- Three odd numbers always add to an odd number, and every odd value from 3 up to 33 can be reached.
- 35 is larger than the biggest possible total of 33, so it can never be made: 35 (E).
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