Brain Teasers
Tennis Balls 2
You have 27 tennis balls. One is heavier than all the others, which all weigh the same. Using the scale which you have, what is the minimum amount of weighings you must make to determine with all certainty which is the heavier tennis ball?
Hint
Think about grouping the tennis balls...Answer
You only have to use the scale 3 times:First, divide the balls into three groups of nine each.
Then, weigh two of the groups on the scale separately. If there is a large difference, then the heavier group has the heavier ball in it. If they are the same weight, then the third group must have the heavier ball in it.
Third, divide this group into three smaller groups of three tennis balls each. Again, weigh two of them separately.
Once you have identified the cluster of tennis balls with the greatest weight, for the third time compare two of the tennis balls. Using the logic as in the first and second steps, you can now define the heaviest tennis ball!
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Comments
Wait, doesn't this mean you'd have to weigh a group of tennis balls, 6 times and not 3 times? If you count each time you use the scale as a discrete, independent event, then it is 6 times that the scale gets used.
You're thinking of the wrong kind of scale. The scale in the problem is the one that just weighs two things against each other (the law scales, if that helps).
Very nice teaser by the way (got it!)
Very nice teaser by the way (got it!)
Your both right ,6 would be the answer on a regular scale and 3 on a [balancing] scale. The type of scale should have been included in the question.I hate when that happens
Sorry. It is a weighing scale. I should have made that clear..
Well, I was a bit stumped because I was using a regular scale, but regardless, I still didn't get the right answer. Started by dividing the group in two and weighing each group separately...
Fun to work on.
Fun to work on.
Thanks a lot.
I also thought of a weight scale instead of a ratio scale. I'm embarrassed to admit it took me more than a second to understand how you got only 3 when your own instructions had 6.
Getting the scale difference was a teaser all by itself
Getting the scale difference was a teaser all by itself
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