Problem 14 · 2019 Math Kangaroo
Medium
Algebra & Patterns
place-valuecasework
Steven wants to write each of the digits 2, 0, 1 and 9 into the boxes of this addition (a three-digit number plus a single-digit number). He wants to obtain the biggest result possible. Which digit does he have to use for the single-digit number?
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Answer: A — either 0 or 1
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Hint 1 of 2
The biggest sum comes from putting the largest digit, 9, in the hundreds place of the three-digit number.
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Hint 2 of 2
The single digit and the units of the three-digit number both count once, so swapping them does not change the total.
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Approach: maximise by place value
- Put 9 in the hundreds place; the sum becomes 900 + (tens, units, single from 2,1,0).
- Put 2 in the tens place to add the most: 920 + (remaining 1 and 0).
- The leftover 1 and 0 fill the units and the single-digit number, each adding the same amount.
- So the single digit can be either 0 or 1: answer A.
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