Results 1 to 2 of 2

Math Help - Largest possible value?

  1. #1
    Newbie
    Joined
    Feb 2008
    From
    Auckland, NZ
    Posts
    16

    Wink Largest possible value?

    For any positive integer N, consider the digits which occur either in N or in 7*N. Let m be the smallest digit among those digits. What is the largest possible value of m?
    Follow Math Help Forum on Facebook and Google+

  2. #2
    MHF Contributor Quick's Avatar
    Joined
    May 2006
    From
    New England
    Posts
    1,024
    Quote Originally Posted by clarebear14 View Post
    For any positive integer N, consider the digits which occur either in N or in 7*N. Let m be the smallest digit among those digits. What is the largest possible value of m?
    You by far have the oddest problems presented, and I need practice because my hw is going to be basically two of these a night

    The answer is 6.

    here's the proof:

    2*7 = 14 so any number that starts with 2, will have a 1 carried over to the next place. Example: 28394*7 = 198758 <-- 7*N will always start with 1 if N starts with 2

    3*7 = 21 so if N starts with 3 then 7*N starts with 2

    here's the whole list:

    2 --> 1
    3 --> 2
    4 --> 2
    5 --> 3
    6 --> 4
    7 --> 4
    8 --> 5
    9 --> 6

    Now it's important to note here that there are two exceptions to this rule, when N starts with 1 then it can be anything, because numbers can carry over, but if N starts with 1 then m would be 1 so no possible value of N starts with 1.

    The second is that there can be a number which carries over. However, because that number would be the first digit of one one digit number times 7 and the second digit of another one digit number times 7 with possibly a one carried on top of it, the highest the second digit of 7*N could be if it sent a carry-over to the first number and the first digit is at least 7 would be: 0

    That sounded really confusing I know.

    Anyway, here's the deal. The highest starting number in 7*N is 7, but that would mean that there is a 0 in 7*n so m would equal 0, that means that the starting number is less than 7 so m is less than 7. It so happens that m can equal 6 and here's an example:

    N = 97
    7*N = 679
    m = 6
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. largest
    Posted in the Differential Geometry Forum
    Replies: 5
    Last Post: May 30th 2009, 07:37 AM
  2. largest value
    Posted in the Algebra Forum
    Replies: 1
    Last Post: December 31st 2008, 04:56 AM
  3. Largest Possible y Value
    Posted in the Algebra Forum
    Replies: 4
    Last Post: December 21st 2008, 07:09 PM
  4. Largest sum
    Posted in the Math Topics Forum
    Replies: 1
    Last Post: September 3rd 2008, 09:17 PM
  5. which one is largest
    Posted in the Algebra Forum
    Replies: 1
    Last Post: August 1st 2005, 04:52 PM

Search Tags


/mathhelpforum @mathhelpforum