Numbers with 0

Number Theory Level 3

How many 9 digit natural numbers have at least one digit that is zero, or has repeated digits.

Note: for this question, 1 = 000000001, and therefore contains zeroes.


The answer is 999637119.

Solden Stoll by Solden Stoll , 16, USA

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1 solution

Solden Stoll
Apr 29, 2019

Note that there are 9 ! 9! ways to organize 9 digits (excluding 0 and repeating digits), and there are 999,999,999 9 digit natural numbers.

999999999 − 9 ! = 999637119 999999999 - 9! = 999637119

0 Helpful 0 Interesting 0 Brilliant 0 Confused

9! gives 9 digit numbers (excluding 0) that have no repeated digit, so u are ignoring numbers like 222222222. Tell me if I'm wrong.. The answer should be something like 1 0 9 − 9 9 10^9-9^9

A Former Brilliant Member - 2 years, 1 month ago

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Oh. I didn't think of that. I'll change the question.

Solden Stoll - 2 years, 1 month ago

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