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Problem #69 · October 4, 2026

Natural numbers

How many three-digit numbers have a digit sum equal to 2626?
  1. A11
  2. B22
  3. C33
  4. D44
  5. E66

WORKED EXAMPLE

Solution

The sum of three digits is at most 9+9+9=279 + 9 + 9 = 27. The only way to obtain 2626 is with the digits 9,9,89, 9, 8. The digit 88 can stand in the ones, tens, or hundreds place, so there are 33 such numbers: 998,989,899998, 989, 899.
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