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Which is Which (Posted on 2006-07-07) Difficulty: 3 of 5
You have six balls - three red and three black. All the red balls weigh differently, i.e. one of them is heavy, the other medium, and the third light. Each red ball has a black twin of the same weight. A heavy and a light ball put together weigh as much as two medium balls.

What is the least number of weighings required on a balancing scale to determine which is which?

No Solution Yet Submitted by Salil    
Rating: 3.0000 (2 votes)

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Solution Solution (at least I'd like to think so.) | Comment 4 of 14 |

Four was the least number that I found.
But there can also be five.

(the numbers after the colors have nothing to do with the weight of the balls)

First senario:

1) red1 vs. black1 ---> red1 > or < black1
2) red2 vs. black1 ---> red2 > or < black1
   (red3 = black 1) = middle weight
3) red1 vs. red 2 ---> red1 > or < red2
   either red1 is the heaviest or red2 is.
4) heaviest red vs. black2 ---> heaviest red = or > black2
   if they are equal, black2 is the heavest, if they're not, black3 is the heaviest.

Senario 2:

1,2&3)Measure all the red balls against each other to find their order.
4&5)Measure two of the black with the middle red ball.
this way you'll get the order for both red and black balls.


  Posted by Liz on 2006-07-08 00:06:59
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