Weighty Balls

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You have eight balls all of the same size. 7 of them weigh the same, and one of them weighs slightly more. How can you find the ball that is heavier by using a balance and only two weighings?

 

 

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Solution

Weigh 3 balls vs 3 balls.

If one side is heavier, weigh one vs one of those three.  If they are equal, the third is the heavier one (and if not, the heavier is heavier).

If the 3 vs 3 is equal, weigh the two remaining balls and see which is the heaviest!



Difficulty
  • Moderate
Type
  • Logic
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Comments

Choose 6 balls and weigh 3 against 3
If they weigh the same, you have another weighing for the remaining 2 balls and you can find the heavier one
If they don'tt weigh the same, from the group of 3 which was heavier, choose any 2 balls and weigh them:
If they weigh the same, the remaining ball is the heavier one; otherwise you just found the heavier one by weighing the 2 chosen balls
- Black Rose (7 May 2009)

The question doesn't indicate whether how many balls can be used in measuring them so why not putting 4 vs 4, then after finding the heavier set of balls, make a 2 vs 2, then find the heavier set and then 1 vs 1 and see what is the heavier one.
- Scorpion (Get Over Here!!!) (10 Apr 2010)

uhhhh, scorpion, you only get 2 TWO weighs. . . .If you weigh 4v4 then 2v2 then 1v1, call me crazy, but i do beleive thats 3 weighs. . . I guess part of figuring out the answer to the question would be reading the question. . .correctly!
- lee (22 Sep 2010)

Technically the answer given doesn't work. If you weigh 3 vs. 3 and one side is heavier. Then you have one more weigh. You can't do 2 vs. 2 because if they still weigh differently then you only know that ONE of the two on the heavier side is the heavier ball(but you don't know which one exactly) If you measure 1 vs. 1 and it come out equal(for the 2nd weigh) then you know that it's one of the OTHER two(from the heavy side in the 1st weigh) and not the one you just weighed. You can only know for sure if you were lucky enough to pick up the heaviest ball and use it for 1 vs. 1 on weigh #2. Otherwise, you're still stuck with 2 that you don't know which one is heavier(or in turn, the heaviest)
- Bre (9 Jul 2011)

Bre, you're not meant to do the 2vs2 after the 3vs3, you're meant to do the 1vs1
- mash (26 Jul 2011)

You could actually do this with 9 balls instead of 8. Think about it.
- Amekne (25 Mar 2013)

Scorpion and Bre, are you kidding me? I know the comments are really old, but I happened upon them reading an article. I just couldn't read what you two wrote and not comment. I certainly hope by now that you get this.
- TrialByAmbush (8 Jun 2015)

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