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Number Theory
Level
3
A book have 273 pages. Find the number of digits used for the numbering of all the pages.
The answer is 711.
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1 solution
There are 273 numbers beginning from 1 to 273.
1-10= 11 digits 1, 11-90=80*2=160 digits, 91-100=21 digits
Total = 11+21+160 =192 digits
Now, Numbers from 101-273 counts to 173 and each number has 3 digits. Therefore, If we break it even further,
101-200 = 100 number 100*3=300 digits
201-273= 73 number 73*3 =219 digits
Final Total = 192+300+219= 711 Digits.
Although, right now I am thinking of a General Solution, but this is how I thought about it.