Determine relative density qualitatively?

[yoyopizza]

So here is the problem, you are given four liquids, each has a different density. You are not allowed to measure the mass, or the volume. You cannot use any numbers. You have to make an educated guess as to which liquid is denser. The liquids are different colors, so if you pour them into a test tube one will float atop the other, but if you pour a denser liquid onto one less dense, they will mix. Good Luck, and thank you soo much to anyone who answers this question with any real ideas. Will post back telling you if it worked :).
You cannot use any math. (I know, it would be so easy otherwise)

I have thought that testing two solutions together and seeing if one would float, because then at least I would have eliminated some of the 24 possible answers, but is it possible to narrow it down further?

 

[tms]

The problem tells you how to proceed: see what floats and what doesn't when one liquid is poured into another.

 

[yoyopizza]

I would love to try that, except I am given a very limited supply of the liquid for that very reason. I am beginning to think this not possible... You just have to get lucky and guess right.

 

[tms]

I would love to try that, except I am given a very limited supply of the liquid for that very reason.

You didn't say that; you've got to give all the information you have if you aren't going to waste people's time.

How limited?

 

[yoyopizza]

I figured out how to narrow down the possibilities a lot, if i take substance 1 and then pour in substance 2, I will then know which is denser. (if they mix substance 2 is denser, if not substance 1). That takes out half of the possible answers. Repeat with 3 and 4, until out of substances. This was the best possible way I could think of to narrow down the possibilities.

 

[yoyopizza]

You didn't say that; you've got to give all the information you have if you aren't going to waste people's time.

How limited?

Sorry about that, didn't realize i didn't tell you. I not told the exact amount, but i will get approx 100mL, 50mL mabye.

 

[tms]

You're on the right track. You start with 16 possible ways to mix one fluid with another. From that you can subtract the 4 that involve mixing a fluid with itself, leaving 12. You can also eliminate half of the rest, because putting A into B gives no more information if you have already put B into A. That leaves 6 tests to do. It may be possible to eliminate more, depending on the results. That is, if you know that A is denser than B, and B is denser than C, you don't have to test A in C.

 

[yoyopizza]

Yes, it worked, since every time i tested it, it would divided the 24 possible answers in half. Thanks.