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)
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.
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