Wednesday, December 23, 2009

How Many Societies Just Give Tractors Away?

There are 3 societies A,B,C having some tractors each.
  • A gives B and C as many tractors as they already have.
  • After some days B gives A and C as many tractors as they have.
  • After some days C gives A and B as many tractors as they have.
  • Finally each has 24 tractors.

What is the original number of tractors each had in the beginning?

Submitted by Guess the Logo.


  1. A had 39 tractors, B had 21, C had 12.

    This is easiest to figure out if you start the math from the end result and work backwards.

  2. I also worked backwards but got a slightly different answer:

    A: 40, B: 22, C: 12

  3. Carol, you have too many tractors. In your response, you have 40+22+12=74. There need to be 72 tractors total (24x3=72.)

  4. After round 3
    a b c
    24 24 24

    A and B both doubled in round 3, so slice them in half to get A and B and subtract from total 72 to get C. That means that the previous nubers must be...

    after round 2
    a b c
    12 12 48

    A and C both doubled in round 2, so the previous numbers were...

    after round 1
    a b c
    6 42 24

    Rinse and repeat with B and C

    a b c
    39 21 12

  5. As Jolson laid out so carefully:
    A 39
    B 21
    C 12


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