All of the Integers from $1$ to $199$, how many times is $1$" used?"
Given: Numbers from $1$ to $199$.
To do: To find that how many times $1$ is used from $1$ to $199$.
Solution:
From $1$ to $99$:
$1,\ 11,\ 21,\ 31,\ 41,\ 51,\ 61,\ 71,\ 81,\ 91$ $1$ is used $10$ times in unit digit
$10,\ 11,\ 12,\ 13,\ 14,\ 15,\ 16,\ 17,\ 18,\ 19$ $1$ is used $10$ times in ten's Digit
Therefore, from $1$ to $99$, $1$ is used $10+10=20$ times.
And this will repeat from $100$ to $199$ too,
Therefore, $1$ is used $20$ times in units & tens Digit place
$1$ will be used $20+20=40$ times.
$1$ will be $100$ times at $100$ place
Hence, In writhing all of the integers from $1$ to $199$, $1$ is used$=100+40=140$ times
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