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Find the number of times the digit $9$ appears in the list of all integers from $1$ to $150$. (The number $ 99 $, for example, is counted twice, because $9$ appears two times in it.)

 Aug 14, 2023
 #1
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To find the number of times the digit 9 appears in the list of all integers from 1 to 150, we can consider the following: 1. Count the number of times 9 appears as the units digit: It appears 15 times (9, 19, 29, ..., 149). 2. Count the number of times 9 appears as the tens digit: It appears 15 times (90, 91, 92, ..., 99, 109, 119, ..., 149). Therefore, the digit 9 appears a total of 15 + 15 = 30 times in the list of all integers from 1 to 150.

 Aug 14, 2023
 #2
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Just list all the numbers with a 9 in them and then count them:

 

9, 19, 29, 39, 49, 59, 69, 79, 89, 90, 91, 92, 93, 94, 95, 96, 97, 98, 99, 109, 119, 129, 139, 149> Total  = 25 "nines"

 Aug 14, 2023

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