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?
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 20060708 00:06:59 