Question

What is the 1000th positive integer with an odd number of digits

Answer 1

Start with 999. That's one of them. Step down until you reach 100. Subtract all the smaller ones, and we have 900 left. Add back 1, 3, 5, 7, and 9. Now we have 905 of them so far, so we have to go back up and find some more past 999. The next one past 999 is 10,000. That's one more. Now we have 906, and we need 94 more. Add 94 to 10,000, bringing us to . . . . . 10,094 . That's my answer and I'm sticking to it ... at least until somebody comes along and shows us the one that's actually correct.

Answer 2

Finding the 1000th positive integer with an odd number of digits.

Positive integers would start from 1.

From 1, 2, 3, 4, ...., 9 This has odd number of digits which is 1 digit. Number of digits = (9 + 1) - 1 = 9.

From 10, 11, 12,......, 99 Has 2 digits, it is not odd number of digits. So it is exempted.

From 100, 101, 102, 103, ......, 999, This has odd number of digits which is 3. Number of digits = (999+ 1) - 100 = 900
Total = 900 + 9 = 909

Number left = 1000 - 909 = 91.

From 1000, 1001, 1002, 1003,......., 9999 would be exempted because it has 4 digits and it is not odd number of digits.

Recall there are 91 left.

From 10000 has odd number of digits which is 5.

From 10000, 10001, 10002, 10003, 10004,......., 10090

Number = (10090 + 1) - 10000 = 91.

So the 1000th positive integer with odd number of digits is 10090