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Problem #15 · August 11, 2026

Natural numbers

How many three-digit numbers can be written using only the digits 00 and 55? (Digits may be repeated.)
  1. A22
  2. B44
  3. C66
  4. D88
  5. E99

WORKED EXAMPLE

Solution

A three-digit number cannot start with zero, so the hundreds digit must be 55. Each of the tens and units digits can be 00 or 55 — 22 choices for each. In total, there are 1⋅2⋅2=41\cdot2\cdot2 = 4 numbers: 500, 505, 550, 555500,\ 505,\ 550,\ 555.
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