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How many 3-digit numbers contain exactly one 0? Examples include 510 and 770.

 Jun 12, 2021
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Let's see...

 

The first digit of a three-digit number obviously can't be $0$. 

 

Let's count the number of $0$ in the numbers $100 - 199$, as then we could just multiply by $9$ to get our result. 

 

For the case $101$, we have the numbers from $101 - 109$, which means there are $9$ numbers. 

 

For the case $110$, we can change the middle digit from $1-9$, (Eg: 110, 120, 130... 190), meaning there are also $9$ numbers. 

 

Thus, from $100-199$, there are $18$ numbers with exactly $1$ zero. Can you solve the problem from here? 

 Jun 12, 2021
edited by xCorrosive  Jun 12, 2021

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