Problem 22 · 2016 Math Kangaroo
Stretch
Number Theory
casework
What is the biggest remainder one can obtain by dividing a two-digit number by the sum of its digits?
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Answer: C — 15
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Hint 1 of 2
The remainder must be smaller than the digit sum you divide by.
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Hint 2 of 2
Test two-digit numbers with a large digit sum that are not multiples of it.
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Approach: maximise the remainder
- The remainder is always less than the digit sum, which is at most 18.
- Trying 79: digit sum 16 and 79 = 4×16 + 15, a remainder of 15.
- No two-digit number does better, so the biggest remainder is 15.
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