Problem 9 · 2011 Math Kangaroo
Medium
Number Theory
digit-sumplace-value
From all whole numbers between 100 and 1000 whose digits sum to 8, the smallest and the largest number are chosen. How big is the sum of those two numbers?
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Answer: B — 907
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Hint 1 of 2
To make the smallest number, keep the hundreds digit tiny; to make the largest, make it big.
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Hint 2 of 2
Find 107 and 800, then add them.
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Approach: find the smallest and largest 3-digit numbers with digit sum 8
- Smallest such number puts weight at the end: 107 (1+0+7=8).
- Largest puts weight at the front: 800 (8+0+0=8).
- Their sum is 107+800 = 907.
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