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We have 10 identical bottles of identical pills (each bottle contain hundred of pills). Out of 10 bottles 9 have 1 gram of pills but 1 bottle has pills of weight of 1.1 gram. Given a measurement scale, how would you find the heavy bottle? You can use the scale only once.

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marked as duplicate by Sconibulus, Community Feb 5 '18 at 15:09

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Add one pill from the first bottle, two from the second, etc.
The decimal digit is the bottle number of the fake pill (with 0 being the 10th bottle)

  • $\begingroup$ @Lolgast, Thanks, spoiler tags seem temperamental on my phone I'm afraid. $\endgroup$ – Fifth_H0r5eman Feb 5 '18 at 15:03
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    $\begingroup$ No problem, quite a few people have problems with them :P The trick is that you can only have consecutive lines starting with >! and a blank line if there is any text following the spoiler. You can add double spaces to the end of your line to create a line break. $\endgroup$ – Lolgast Feb 5 '18 at 15:07
  • $\begingroup$ Or a HTML line break <br> without needing to type even a return. $\endgroup$ – Mr Lister Feb 5 '18 at 16:04

When adding the bottles to the scale make sure to switch the side you put them on with every bottle. Once one side is tipping down you have your bottle. It's the last one added.

That is if adding them individually counts as only using the scale once.

  • $\begingroup$ Assuming our scale was a balance then if you are noting its position after each time you put a bottle on then I would say that is more than one weighing. Additionally after you put one bottle on that side has tipped down which would mean by your wording that the first one (which is the last one added when one side goes down) is the heavy one which is not the case. Also I think when the OP said a measurement scale they meant something that would give a weight for the items placed on it and not a balance which allows you to compare relative weight of two things. $\endgroup$ – Chris Feb 5 '18 at 16:06
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    $\begingroup$ Yeah it kinda felt too easy. Obviously I meant every other bottle. ;) But you are right. I didn't know the difference in scale and measurement scale, thanks for pointing that out. The other answer is more elegant anyway and definately needs only one time weighting, so I guess it's correct. :) $\endgroup$ – Morfium Feb 5 '18 at 16:16

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