We have nine balls where three of them weigh x grams, three of them weigh y grams and three of them weigh z grams with
x > y > z. Using a balance scale, we want to determine which group each ball belongs to(in other words, whether it weighs x, y or z grams). What is the smallest number of weighings that guarantees us such a finding?
2007-08-31 08:35:29 · 6 answers · asked by bilgilikisi 1 in Science & Mathematics ➔ Mathematics
With the assumption made, I agree with Tom's procedure but what question asks is a different thing.While trying to determine the group of each ball, we should consider the worst(the most unlucky) scenario that allows us to get the weighings and thus this supposition does not work.
2007-08-31 09:31:45 · update #1
Not a best case senario!
14 weighs.
First weigh one ball to all others.and name threes
Second weights one of the others with all remaining.
Example xxx yyy zzz
choose x and weigh it with all other so find xxx
choose y or z and weigh it with remainig so find yyy and zzz
Best case senario!
In case you are lucky and choose xxx yyy and zzz in this order, then it would be 4 weighs, because if you find 3 same balls then you should change to another ball and weigh this instead of the first. When you weigh 3 y's then you stop.
2007-09-07 04:33:27 · answer #1 · answered by Anonymous · 1⤊ 0⤋
In a best-case scenario, you can determine the relative positions of 3 balls in 3 weighings; this presumes that you managed to grab one x, one y, and one z ball at random.
Once that is done, the best case scenario again is that you pick a y-ball against which to measure the others. If it's lighter then it's an x, if equal it is y, and if heavier it is z.
There are 6 balls remaining. If you pick both x's and both z's (4 weighings total), then the last 2 balls are both y.
Minimum number of weighings: 7.
edit: Tom's answer is correct, but presumes you know what kind of ball you have at the beginning. I didn't.
2007-08-31 16:24:04 · answer #2 · answered by Mathsorcerer 7 · 0⤊ 0⤋
it's 6..
6>2>1
2007-09-08 04:55:23 · answer #3 · answered by jaycellann_20 2 · 0⤊ 0⤋
The min would be 5. This would assume you used a "y" ball to meause and found the 3 "z"s and then found the two "y"s and the remaining are "x".
Unless you have more constraints, the answer is 5!
2007-08-31 16:15:53 · answer #4 · answered by Tom . 2 · 0⤊ 0⤋
THE ANSWER IS ONE IF YOU TAKE ONE BALL FROM X GROUP TWO FROM Y GROUP AND THREE FROM Z GROUP WEIGH THEM ALL AT ONCE AND DETERMINE WHICH GROUP IS WHICH BY TOTAL ie 6GRAMS PLUS 2 Y 6GRAMS PLUS3X ETC
2007-09-06 15:21:31 · answer #5 · answered by Anonymous · 0⤊ 0⤋
i have nine balls too! exciting huh!! heh this shits to hard
2007-09-04 20:32:44 · answer #6 · answered by </3 2 · 0⤊ 2⤋