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How many integers in the set {100, 101, 102, ..., 999} have at least one digit repeated?

Updated On: Jan 15, 2026
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Solution and Explanation

The total count of 3-digit integers is derived as:
\(= 999 - 100 + 1 = 900\)

Let \(N\) represent the count of 3-digit integers with unique digits.

Digits are selected from the set {0, 1, 2, ..., 9}, comprising 10 distinct digits. 
For a 3-digit number, the following constraints apply:

  • The hundreds digit (the first digit) cannot be 0. This leaves 9 possible choices (digits 1 through 9).
  • After selecting the first digit, there are 9 remaining digits available for the tens digit, as the digit used in the hundreds place is excluded.
  • Following the selection of the first two digits, there are 8 digits available for the units digit.

 

Consequently, the count of 3-digit integers where all digits are distinct is:  
\(N = 9 \times 9 \times 8 = 648\)

Therefore, the count of 3-digit integers with at least one repeated digit is calculated as:  
\(= 900 - 648 = 252\)

Final Answer: \(\boxed{252}\)

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