Question

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 1

When 3 is the hundreds digit, meaning 300 to 303, there are 4 pages with total of 5 times digit 3 printed (i.e. 300, 301, 302, 303 <== 2 3's from 303)

When 3 is the tens digit, 
p. 30 - 39 ---------- 10 pages with 11 3's (extra 3 from 33)
p. 130 - 139 ------- 10 pages with 11 3's (extra 3 from 133)
p. 230 - 239 ------- 10 pages with 11 3's (extra 3 from 233)

When 3 is the units digit, (e.g. 3, 13, 23,... )
p. 1 - 99 ----------- 9 pages with 9 3's (originally there are 10 pages with 11's but need to take away 33 as we already counted it)
p. 100 - 199 ------ 9 pages with 9 3's (excluded 133)
p. 200 - 299 ------ 9 pages with 9 3's (excluded 233)

So the total number of 3's printed is 5+11+11+11+9+9+9 = 65

For, pages with only one 3
P. 300 - 303 ------ 4 pages

When 3 is the tens digit, 
p. 30 - 39 ---------- 9 pages (exclude 33)
p. 130 - 139 ------- 9 pages (exclude 133)
p. 230 - 239 ------- 9 pages (exclude 233)

When 3 is the units digit, (e.g. 3, 13, 23,... )
p. 1 - 99 ----------- 9 pages (exclude 33)
p. 100 - 199 ------ 9 pages (excluded 133)
p. 200 - 299 ------ 9 pages (excluded 233)

So the total number of pages that only has one 3 = 4 + 3* 9 + 3*9 = 58