George is reading a novel which has 303 pages. how many times does the digit 3 get printed in the page numbers? how many pages are there which has only one 3 present in the page number?

George is reading a novel which has 303 pages. how many times does the

1.	George is reading a novel which has 303 pages. how many times does the digit 3 get printed in the page numbers? how many pages are there which has only one 3 present in the page number?
Answer» Case 1: numbers with 3 are like 3,13,23,......,303 they are in AP with a=3, d=10 let the total number of pages with the DIGIT 3 be N. 303 = 3 + (n-1)10 ⇒ n-1 = 300/10 = 30 ⇒ n = 31 number of pages = 31 case 2: number like 30,31,...39; 130,131,...139; 230,231,...239 from 30 to 39 - there are 10 numbers from 130 to 139 - there are 10 numbers from 230 to 239 - there are 10 numbers total = 10+10+10 = 30 but we have already counted 33,133 and 233. so number of pages = 30-3 = 27 case 3: the number 300,301 and 302. (303 has already been counted) so numbers = 3 So total number of pages = 31+27+3 = 61 every number having three has only one three except 33,133,233 and 303. number of pages with 2 threes = 4 number of pages with only one three = 61 - 4 = 57 total number of PRINTING of 3 = 57×1 +4×2 = 57+8 = 65. So the digit 3 has been printed 65 times and number of pages with only one 3 present is 57.