Pills o' poison

[h4tt3n]

Consider ten identical glass bottles of pills. Each bottle contains one hundred pills. Nine bottles contain poisonous pills. One bottle contains harmless pills. The poisonous and harmless pills are identical in every way except that the harmless ones weigh 1.1 g and the poisonous ones only weigh 1.0 g.

 

Figure out which bottle holds the harmless pills. Your only tool is a table top scales, and you are allowed only one weighing.

Edited July 9, 2008 by h4tt3n

[Cap'n Refsmmat]

I presume each bottle of pills contains an identical quantity of pills and that the bottle without poisonous pills is filled with harmless pills?

[h4tt3n]

I presume each bottle of pills contains an identical quantity of pills...

 

Yes. Let's just say that each bottle contains one hundred pills.

 

...and that the bottle without poisonous pills is filled with harmless pills?

 

I wasn't quite clear about that, but yes it does.

 

(I will edit the IP accordingly, in order to clarify the puzzle.)

Edited July 9, 2008 by h4tt3n

[Cap'n Refsmmat]

And by scales do you mean a balance or a scale that takes one item at a time?

[h4tt3n]

And by scales do you mean a balance or a scale that takes one item at a time?

 

By specifically using the word "table top scales" I was hoping that it'd be clear that I ment something like this:

 

http://product-image.tradeindia.com/00008118/b/Table-Top-Scales-with-Flat-Bowl.jpg

 

The container at the top may hold an unlimited number of pills.

[YT2095]

any limit as to how fast you can fill the bowl of these scales up?

 

could I take one pill out of bottle one and put that in and then another from bottle 2 and so on, and wait for a 1.1 jump in the gram count?

[h4tt3n]

...could I take one pill out of bottle one and put that in and then another from bottle 2 and so on, and wait for a 1.1 jump in the gram count?

 

No. That would be considered more than one weighing, which is not allowed.

[Phi for All]

any limit as to how fast you can fill the bowl of these scales up?

 

could I take one pill out of bottle one and put that in and then another from bottle 2 and so on, and wait for a 1.1 jump in the gram count?

This was my first thought too. Especially after seeing the scale (I was originally thinking balance like Cap'n). "I'm gonna put all these bottles on here to be weighed... one at a time!"

 

Since you can't possibly pick one bottle from ten by weight in one weighing, and I assume that you won't be able to tell if one bottle weighs 100 grams and another weighs 110 grams just by the feel of it, the poison part must come into play somehow. I had almost written that off as a red herring, since self-testing seemed ill-advised. But is the poison a lethal one? If so, is it lethal at any dose? Could I test a fragment of a pill (just crush it with the scale, lol), wait for any ill effect and repeat until there was none, seeing as time is not limited for this experiment?

[YT2095]

are you allowed to use your Hands to weigh them then?

10g is quite noticable, so if you weigh One (any one) you`ll have a KNOWN weight to work with and compare to.

[John Cuthber]

"The poisonous and harmless pills are identical in every way except that the harmless ones weigh 1.1 g and the poisonous ones only weigh 1.0 g. "

That seems odd- surely one important distinction (in addition to the difference in mass) is that one set of pills is toxic and the other isn't.

Did you mean that the pills seem identical...

 

Anyway, if you take one pill from the first bottle, two pills from the second bottle and so on, put them all together on the scale and weigh them.

If the first bottle's not the poison you get 1.1+2+3+4...=45.1 g .

If it's the second bottle you get 1+2.2+3+4+...=45.2g

The difference between the mass and the nearest integer below is the number of the bottle with the non poison pills.

[h4tt3n]

Could I test a fragment of a pill (just crush it with the scale, lol), wait for any ill effect and repeat until there was none, seeing as time is not limited for this experiment?

 

No.

 

are you allowed to use your Hands to weigh them then?

 

No.

 

The only allowed tool is the table top scales.

 

You are allowed to take any number of pills in any desired combination and weigh them once, hereby revealing which bottle contains the harmless pills.

[DrP]

"The poisonous and harmless pills are identical in every way except that the harmless ones weigh 1.1 g and the poisonous ones only weigh 1.0 g. "

That seems odd- surely one important distinction (in addition to the difference in mass) is that one set of pills is toxic and the other isn't.

Did you mean that the pills seem identical...

 

Anyway, if you take one pill from the first bottle, two pills from the second bottle and so on, put them all together on the scale and weigh them.

If the first bottle's not the poison you get 1.1+2+3+4...=45.1 g .

If it's the second bottle you get 1+2.2+3+4+...=45.2g

The difference between the mass and the nearest integer below is the number of the bottle with the non poison pills.

 

Nice one. That would work. I've heard of the problem before but I'd forgotten how to do it.

[h4tt3n]

"The poisonous and harmless pills are identical in every way except that the harmless ones weigh 1.1 g and the poisonous ones only weigh 1.0 g. "

That seems odd- surely one important distinction (in addition to the difference in mass) is that one set of pills is toxic and the other isn't.

Did you mean that the pills seem identical....

 

Pedant!

 

Anyway, if you take one pill from the first bottle, two pills from the second bottle and so on, put them all together on the scale and weigh them.

If the first bottle's not the poison you get 1.1+2+3+4...=45.1 g .

If it's the second bottle you get 1+2.2+3+4+...=45.2g

The difference between the mass and the nearest integer below is the number of the bottle with the non poison pills.

 

Yes, you figured it out. Congrats!

 

(another time, please "hide" the answer so you won't spoil it for the rest.)