LG from PT 12 (Oct. 1994) Forum

[anewaphorist]

The game: "A science student has exactly 4 flasks--1, 2, 3, and 4--originally containing a red, a blue, a green, and an orange chemical, respectively. An experiment consists of mixing exactly two of these chemicals together by completely emptying the contents of one of the flasks into another of the flasks. The following conditions apply:

-The product of an experiment cannot be used in further experiments.
-Mixing the contents of 1 and 2 produces a red chemical.
-Mixing the contents of 2 and 3 produces an orange chemical.
-Mixing the contents of 3 with the contents of either 1 or 4 produces a blue chemical.
-Mixing the contents of 4 with the contents of either 1 or 2 produces a green chemical."

I correctly answered all 7 of the questions associated with this game, except for the last one (which, incidentally, was the last question of the section--#24). I'm worried primarily about how to answer the last question (see below) and secondarily about speeding up my pace on a complicated game like this. Input addressing either concern is greatly appreciated.

Q. 24: "If the student performs exactly two experiments and exactly one of the reslting two nonempty flasks contains an orange chemical, then it must be true that the contents of the other nonempty flask is (sic):"
(A) obtained by mixing flasks 1 and 2
(B) obtained by mixiing flasks 2 and 4
(c) blue
(D) green
(E) red

Correct answer: (D)

I knew that only answers (D) or (A) could satisfy the "must be true" requirement, so I chose (A) because the combination of R (flasks 1 and 2 mixed) G(3) O(4) produces an orange chemical only if flasks 3 (green) and 1/2 (red) are mixed, which produces a blue chemical as the 2nd nonempty flask. All or almost all of the other possible combinations produce a green nonempty flask, so I guess my main question is, how is this question coherent? Have I totally missed something?

[anewaphorist]

So I realized that the "red" chemical produced from experiment 1 cannot be used in the 2nd experiment, so I guess this is the only question in the game in which the 1st rule affects the outcome (or maybe it was just inessential to answering the other 6 questions correctly). Any help with the setup of this game would still be appreciated. Cheers!

[JacobH]

For the last question, if you know there were two experiments done, and one of the resulting colors is orange, then you can basically just look at the rules, go "oh look, 2 + 3 = Orange, then figure out that the only flasks left are 1 and 4, and they make Green".

Here is my setup, very simple:

original: R B G O

1 + 2 = R
2 + 3 = O
3 + 1/4 = B
4 + 1/2 = G