Problem 21 · 2013 Math Kangaroo
Stretch
Number Theory
factorizationdigit-sum
Ralf wants to tell Karl a number whose digits multiply to exactly 24. What is the digit sum of the smallest number Ralf can say?
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Answer: E — 11
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Hint 1 of 2
Find digits whose product is 24, using as few digits as possible.
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Hint 2 of 2
Among same-length numbers, put the smaller digit first to make the number smallest.
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Approach: smallest number with given digit product
- Two single digits can multiply to 24: 4×6 or 3×8.
- The smallest two-digit number from these is 38 (since 38 < 46).
- No one-digit number works, so 38 is the smallest possible number.
- Its digit sum is 3 + 8 = 11.
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