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by alaynaik » Tue Aug 16, 2011 12:59 pm
Hello Guys,
I request you all to help me with the following query:

How many numbers from 1 to 1000, both inclusive, have digits repeated?
Ans. Options--->9,81,262,648,738

Thanks.
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by GmatKiss » Tue Aug 16, 2011 1:52 pm
IMO: 262
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by gmatboost » Wed Aug 17, 2011 2:19 pm
Structured approach:

4 digit numbers: 1000 (1 number), 1 has repeating digits

3 digit numbers: 100-999 (900 numbers)
How many do NOT have repeating digits?
9 choices for first digit (no zero)
9 choices for second digit (not the first one, but zero okay)
8 choices for third digit (not the first two)
9*9*8 = 648 without repetition
900 - 648 = 252 with repetition

2 digit numbers: 10-99 (90 numbers)
How many do NOT have repeating digits?
9 choices for first digit (no zero)
9 choices for second digit (not the first one, but zero okay)
9*9 = 81 without repetition
90 - 81 = 9 with repetition (or you could count 11, 22, 33, ... 99)

1 digit numbers: no repetition

Total with repetition = 1 + 252 + 9
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