Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

Math prob

  1. Feb 13, 2004 #1
    The arithmetic mean of a set of nine different positive integers is 123456789. Each number in the set contains a different number of digits with the greatest value being a nine-digit number. Find the value of each of the nine numbers .
  2. jcsd
  3. Feb 13, 2004 #2
  4. Feb 14, 2004 #3
  5. Feb 14, 2004 #4

    matt grime

    User Avatar
    Science Advisor
    Homework Helper

    The only conceivable way there could be a unique answer is if all the numbers involved had some maximality/minimality conditions imposed on them (ias x+y=x-1+y+1, then any unqueness here must expliot some maximality of y or minimality of x; we have a maxmial number 999,999,999) . By inspection one sees that 123456789*9 can only be the sum of numbers satisfying your conditions if they are maximal wrt the constraints.

    Also it's clear that 123456798
    =1+11+111+1,111+.....111,111,111, which should give another hint
  6. Feb 14, 2004 #5
    I immediately recognized that 123456789 = 1+11+111+1111...111111111, like Grime said. Knowing this, multiply both sides by 9, and find the answer.

    Also like Grime said, the values must be that maximums, which means that there is only one correct answer.
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook

Have something to add?

Similar Discussions: Math prob
  1. Prob. question (Replies: 3)

  2. Current prob (Replies: 1)

  3. Hard matrix prob (Replies: 4)