How many positive integers less than 1020 have all their digits the same? also give the solution kindly,,,,,,,,,and thanx a lot for the last question's answer
1,2...9
11,22...99
111,222...999
Looks like 27 to me
why specify 1020? odd upper limit.
10^20 ??not 1020
20*9=180
To find the number of positive integers less than 1020 with all their digits the same, we need to consider the possible values for the repeated digit.
There are 10 possible digits (0-9), so we can consider each digit (from 0 to 9) separately and count the numbers that satisfy the condition.
Let's examine each digit:
1. For the digit 0:
- Since we are looking for numbers less than 1020, the first digit cannot be zero. So there are no numbers with all digits being 0.
2. For the digits 1 to 9:
- For each digit, we have one possible number: 111, 222, 333, and so on.
- However, we need to ensure that the number is less than 1020, so we need to consider the restrictions for each digit:
- For digit 1: We can have 111, which is less than 1020.
- For digits 2 to 9: We can only have 222, 333, ..., 999 since all the digits are the same.
- So there are a total of 9 numbers, one for each digit from 1 to 9.
Therefore, there are a total of 9 positive integers less than 1020 that have all their digits the same.
Solution:
The solution is simply 9.