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Redundant Digits

Redundant Digits

Posers and Puzzles

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How many integers between 1000 and 9999 inclusive have at least one repeated digit?

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@joe-shmo said
How many integers between 1000 and 9999 inclusive have at least one repeated digit?
Do numbers like 1030 count? [two zeros, but not back-to-back]

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@bigdoggproblem said
Do numbers like 1030 count? [two zeros, but not back-to-back]
Yeah, the 0 is considered a repeated digit in your example.

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@joe-shmo said
How many integers between 1000 and 9999 inclusive have at least one repeated digit?
Easiest approach to this is to find how many DON'T have a repeat.

10x9x8x7=5040

9999-1000=8999

8999-5040=***3959***

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@AThousandYoung

The method is right, but there are two errors in the arithmetic.

1)

There are 9999-1000+1 = 9000 total numbers (do not forget to count the number 1000 also).


2)
The thousands digit has only NINE possibilities; it cannot be 0. 9*9*8*7 = 4536


Solution:
9000 - 4536 = 4464

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@BigDoggProblem

Correct!