## 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.

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

originally
a b c
39 21 12

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

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