1. Limited time only! Sign up for a free 30min personal tutor trial with Chegg Tutors
    Dismiss Notice
Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

Consecutive and minimum pair puzzle

  1. Feb 23, 2009 #1
    Two consecutive positive decimal integers are such that the sum of the digits of each of them is divisible by 11.

    Determine the minimum possible pair of such numbers.
  2. jcsd
  3. Feb 25, 2009 #2
    Let the 2 numbers be:
    t...x y z 99...9
    t...x y (z+1) 00...0

    Suppose n 9's.
    Then 9*n-1 is divisible by 11.
    So, n=5.
    We know the first number is
    t...x y z 99999
    But t+...+x+y+z = 55-45=10. So, the numbers are
    2899999 and 2900000

Share this great discussion with others via Reddit, Google+, Twitter, or Facebook