Combinatorics
Probability
Level
pending
How many times is the digit 0 written when listing all numbers from 1 to 3333?
The answer is 963.
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1 solution
consider the following type/ range / #s / # of digits / # of o's A / 0 - 9 / 10 / 10 / 1 B / 00 - 99 / 100 / 200 / 20 C / 000 - 999 / 1000 / 3000 / 300 as can be seen, # of 0's = 1/10 * number of digits
now come to the problem (x's denote digits that can range from 0 to 9) 10 - 99 => 1x to 9x => type A = 9 1 = 9 100 - 999 => 1xx to 9xx => type B = 9 20 = 180
1000 - 2999 => 1xxx to 2xxx => type C = 2*300 = 600
special treatment 3000 - 3299 => 0xx to 2xx => type B = 3*20 = 60 + 100 for the 0's in the hundreds unit = 160 0's from 3300 to 3333 can just be counted = 14