Question:medium

How many integers in the set {100, 101, 102, ..., 999} have at least one digit repeated?
[This Question was asked as TITA]

Updated On: Jan 15, 2026
  • 252
  • 254
  • 262
  • 264
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The Correct Option is A

Solution and Explanation

The set of integers considered is from 100 to 999, encompassing all 3-digit numbers. The total count of these numbers is calculated as follows:

\[ \text{Total numbers} = 999 - 100 + 1 = 900 \]

The subsequent step involves identifying the count of these numbers that possess no repeated digits. Each 3-digit number comprises a hundreds, tens, and units digit. The determination of such unique combinations is as follows:

  • Hundreds digit: 9 options (digits 1 through 9, as 0 is not permissible)
  • Tens digit: 9 options (the hundreds digit is excluded)
  • Units digit: 8 options (digits used for the hundreds and tens are excluded)

\[ \text{Numbers with all unique digits} = 9 \times 9 \times 8 = 648 \]

Subtracting this value from the total yields the count of numbers with at least one repeated digit:

\[ \text{Repeated digit numbers} = 900 - 648 = \boxed{252} \]

Final Answer:
The quantity of 3-digit numbers exhibiting at least one repeated digit is: \[ \boxed{252} \]

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