Problem 16 · 2015 Math Kangaroo
Medium
Arithmetic & Operations
grouping
There are 10 balls, numbered 0 to 9 in a basket. John and George play a game. Each person is allowed to take three balls from the basket and calculate the total of the numbers on the balls. What is the biggest possible difference between the John and George's totals?
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Answer: E — 21
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Hint 1 of 2
To make the gap as large as possible, one player grabs the biggest numbers and the other the smallest.
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Hint 2 of 2
They draw from the same basket, so the two sets of three balls cannot overlap.
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Approach: maximise one total and minimise the other
- One player can take the three largest balls: 9 + 8 + 7 = 24.
- The other is then left to take the three smallest: 0 + 1 + 2 = 3.
- The biggest possible difference is 24 − 3 = 21.
- The answer is 21.
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