Dewey's Teaser - Oct 22

[Dewey]

Today's puzzle is a math one:

You have five jars of pills. All of the pills in one jar only are "contaminated." The only way to tell which pills are contaminated is by weight. A regular pill weighs 10 grams; a contaminated pill is 9 grams. You are given a scale and allowed to make just one measurement with it. How do you tell wich jar is contaminated?

[CJman327]

AHHHH!!!!! THE MATH! I can't do it! It's the weekend, Dewey!

[CJman327]

Well, how many pills are in all of the jars?

[Emrysgirl]

With 2 measurements is easy, but with one?...you've got me stumped.

[Wildcat]

You've got me on this one too. The contaminated jar is obviously going to weigh less, but I can't figure out how you can tell with only one measurement!

[Dewey]

Answer:

In a more normal situation, you’d probably weigh a pill from each jar until you found one that weighed 9 grams. That won’t work here, since you’ve only got one measurement. Chances are four in five that the first and only pill you weigh will be of normal weight.

That means you must weigh pills from more than one jar in your single measurement. Take the simplest case: You weigh five pills, one from each jar. The result will necessarily be 10 + 10 + 10 + 10 + 9 = 49 grams. The trouble is, you know that before making the measurement. The 49-gram result cannot tell you which bottle contributed the 9-gram pill.

You need to manufacture a situation in which the weight measurement is informative. One solution is to call the bottles #1, #2, #3, #4, and #5. Take one pill from #1, two from #2, three from #3, four from #4 and five from #5. Weigh the whole lot. Were all the pills normal, the result would be 10 + 20 + 30 + 40 + 50 = 150 grams. In fact, the weight must fall short of this by the number of grams equal to the number of the contaminated bottle. Should the total weight be 146 (4 grams short), then bottle #4 must contain the lighter pills.

[samboo1]

You've lost me...

[Wildcat]

Wow, I never would have figured that one out! At least it wasn't something really obvious.

[Emrysgirl]

Good one! I wasn't even thinking of taking the pills out.