Results 1 to 3 of 3

Math Help - Integers

  1. #1
    Newbie
    Joined
    Dec 2005
    Posts
    2

    Integers

    how many integers between 1500 and 8000 (inclusive) contain no repeated digits?
    Follow Math Help Forum on Facebook and Google+

  2. #2
    Newbie krassi_holmz's Avatar
    Joined
    Dec 2005
    Posts
    4
    If we fix first 2 digits we'll get exactly 7*8 numbers with this proprty. So the number of non-repeaters between 1500 and 8000 is equal to the number of non-repeaters between 15 and 80 multiplied by 56. So:
    56(5+9+9+9+9+9+9)=56.59=3304.
    Another way:
    First we'll calculate the number of non-repeaters between 1000 and 1500:
    We have 6 possibilities for the second digit but it's unequal to 1 and 5 so there are 4 real possibilities. For the other two digits we have 8.7 possibilities. So total 8.7.4=224 numbers between 1000 and 1500
    Analogous we have 7.9.8.7=3528 non-repeaters between 1000 and 8000 so we have 3528-224=3304 non-repeaters between 1500 and 8000.
    Last edited by krassi_holmz; December 10th 2005 at 04:21 PM.
    Follow Math Help Forum on Facebook and Google+

  3. #3
    Newbie
    Joined
    Dec 2005
    Posts
    2
    thanks for the help. I already figured it out using the second method you discribed. I still don't understand the first method. is that induction? needless to say I did not figure this out before I handed my test in and I got it wrong.
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. Replies: 2
    Last Post: December 5th 2011, 11:47 PM
  2. Replies: 7
    Last Post: August 3rd 2010, 01:31 PM
  3. Matrix of integers whose inverse is full of integers
    Posted in the Advanced Algebra Forum
    Replies: 2
    Last Post: March 19th 2010, 02:02 PM
  4. Replies: 4
    Last Post: February 24th 2008, 03:08 PM
  5. Replies: 2
    Last Post: October 14th 2007, 03:18 PM

Search Tags


/mathhelpforum @mathhelpforum