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Question

In writing all of the integers from 1 to 199, how many times is '1' used?


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Solution

Step 1: Counting the number of times one occurs from 1 to 99

1,21,31,41,51,61,71,81,919 times in unit digit

10,12,13,14,15,16,17,18,199 times in ten’s Digit

11-2 times ,i.e., at unit and ten's digit

9+9+2=20 times

Step 2: Counting the number of times one occurs from 100 to 199

111will be counted for unit digit, ten's digit and hundred's digit so it will be come 3 times.

101,121,131,141,151,161,171,181,1919 times at unit digit

110,112,113,114,115,116,117,118,1199 times at ten’s Digit

100,102,103,104198,199-81 times at hundred's digit.

81×1+9×2+9×2+3=120 times

Step 3: Number of times one occurs from 100 to 199

120+20=140

Therefore, in all integers from 1 to 199, the total number of times '1' is used is 140 times.


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