how many 2 digit numbers can be written so that the second digit is greater than the digit before it ?
12 through 19 = 8.
23 through 29 = 7.
34 through 39 = 6.
45 through 49 = 5.
56 through 59 = 4.
67 through 69 = 3.
78 through 79 = 2.
89-------- = 1.
Total----- = 36 Numbers.
To find out how many two-digit numbers can be written where the second digit is greater than the digit before it, you can break down the problem into different cases.
CASE 1: The first digit is 1
In this case, the second digit can be any number from 2 to 9. So, there are 8 possible two-digit numbers where the second digit is greater than the digit before it when the first digit is 1 (12, 13, 14, 15, 16, 17, 18, 19).
CASE 2: The first digit is 2
In this case, the second digit can be any number from 3 to 9. So, there are 7 possible two-digit numbers where the second digit is greater than the digit before it when the first digit is 2 (23, 24, 25, 26, 27, 28, 29).
CASE 3: The first digit is 3
In this case, the second digit can be any number from 4 to 9. So, there are 6 possible two-digit numbers where the second digit is greater than the digit before it when the first digit is 3 (34, 35, 36, 37, 38, 39).
Similarly, you can continue with the remaining cases (first digit is 4, 5, 6, 7, 8, 9) and find the count for each case.
Adding up the results from all the cases, you get:
8 + 7 + 6 + 5 + 4 + 3 + 2 + 1 = 36
Therefore, there are 36 two-digit numbers that can be written so that the second digit is greater than the digit before it.