Thread: How many 10 digit positive integers with at most 7 consecutive zeros?

How many 10-digit positive integers with no leading zeros (i.e., integers from 1,000,000,000 to 9,999,999,999) have at most 7 consecutive zeros? For example, the number 3,000,000,200 has 8 zeros but they are not all consecutive and therefore this number should be counted. On the other hand, the number 8,000,000,001 has 8 consecutive zeros and should not be counted.

first find out the number of numbers with exactly 7 consecutive zeros, 8 consecutive zeros and 9 consecutive zeros. sum all these up and subtract from the total number of 10 digit numbers.

in my last post i committed a mistake. you dont have to subtract the number of numbers having exactly 7 consecutive zeros since the question allows the counting of these numbers.

so to get the answer find:
(total number of 10 digit numbers) - [(number of numbers having exactly 8 consecutive zeroes)+(number of numbers having exactly 9 consecutive zeros)]