Integers

How many positive integers are there between 100 and 199 with different digits



    Solution

    Let's get the problem from scratch
    I ask for the integers between 100 and 199 each

        displays different digits

    In the tenth of 100 to 110
   
    I exclude 2 integers that have the same digits ie 101 and 110
    Therefore, there are 8 integers with different digits

    The second tenth of 110 to 120 is excluded as all three-digit numbers display two identical digits

        110,111,112, ..., 119

    In the third tenth of 120 to 130, there are also excluded 2 integers 121 and 122 whereby 8 integers

         with different digits


    Continuing the same procedure (algorithm) I find that for every new tenth there are 8 integers

         with different digits

    In total, from 100 to 199 I have a total of 10 dozen
   
    I exclude the 2nd tier (if the integers have two identical digits)

    So I have 10-1 = 9 tens
    (9 tens) x (8 integers) = 72 integers with different digits

          Stella Seremtaki