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Problem #26 · August 22, 2026

Natural numbers

Find the sum of all four-digit numbers formed by using each of the digits 5,6,7,85, 6, 7, 8 exactly once.
  1. A2888628886
  2. B8665886658
  3. C115544115544
  4. D173136173136
  5. E173316173316

WORKED EXAMPLE

Solution

The four distinct digits form a total of 4!=244! = 24 numbers, and each digit appears in each position 3!=63! = 6 times. Therefore, the sum is 6⋅(5+6+7+8)⋅(1000+100+10+1)=6⋅26⋅1111=1733166\cdot(5+6+7+8)\cdot(1000+100+10+1) = 6\cdot26\cdot1111 = 173316.
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