Nothing Fishy

Logic Level 2

A fishkeeping enthusiast owns $12$ different species of fish. As some species are not compatible with others, he has acclimated them into $4$ fish tanks as follows:

Tank	Species
Tank $1$	$A,D,H$
Tank $2$	$G,I,K$
Tank $3$	$C,E,J$
Tank $4$	$B,F,L$

This morning, one of the fish tanks collapsed but luckily the fishkeeper was able to put the fish that fell on the floor back into the remaining tanks without any compatibility problems or the need to transfer some fish from one tank to another.

By looking at the compatibility table below, can you guess which tank broke ?

Species	is not compatible with
$A$	$B,C,F$
$B$	$E,I$
$C$	$D,G$
$D$	$E,K,L$
$F$	$G,H,I$
$H$	$G,I,J$
$I$	$L$
$J$	$K$
$K$	$L$

Tank 1 Tank 2 Tank 3 Tank 4 Impossible to know

1 solution

Romain Bouchard
Feb 15, 2018

Relevant wiki: Graph Coloring and Chromatic Numbers

If the first tank breaks, species $D$ cannot go elsewhere as it is incompatible with species $K$ in tank $2$ , with species $E$ in tank $3$ and with species $L$ in tank $4$ .

If the second tank breaks, species $G$ cannot go elsewhere as it is incompatible with species $H$ in tank $1$ , with species $C$ in tank $3$ and with species $F$ in tank $4$ .

If the fourth tank breaks, species $B$ cannot go elsewhere as it is incompatible with species $A$ in tank $1$ , with species $I$ in tank $2$ and with species $E$ in tank $3$ .

However, If the third tank breaks, species $C$ and $J$ can go into tank $4$ and species $E$ can go into tank $2$ , hence the answer is $\boxed{tank \space 3}$ .

This is such a "gotcha" question. I noticed that some of the species were missing from the table, and that's fine, because then you'll have to infer their compatibility from the other species that are actually in the table. However, if there is a specific entry for species B and it specifically states that B is incompatible with E or I, then you would assume that it IS compatible with the other species. I say assume, but actually it's not an assumption, because that's how lookup tables work. That's like saying I have two children when someone asks, but then it turns out I actually have three children. Well, I didn't lie, I do still have the first two, don't I? This has nothing to do with logic.

Vadim Evstifeev - 3 years, 2 months ago

Hi. When posting problems I never go for tricky questions or misleading formulations because I feel it is not fair to the people working on them and also because it is against the Brilliant guidelines. If this happens (we're all humans) it is a mistake on my part.

That said :

I categorized this problem as "Discrete Mathematics" when posting it with the idea that people would draw the comptibility graph (species being the vertices and compatibility being the edges, cf. relevant wiki in my solution). As it often happened it has been re-categorized by moderation into "Logic" which I personally do not agree either .
I don't understand where the problem misled you : $B$ IS indeed compatible with all species other than $E$ , $I$ and $A$ as specified in the table and as you correctly figured. Do you mean that the incompatibility between $B$ and $A$ is not clearly specified because it is in the first row only and not repeated again in the second row ?

Romain Bouchard - 3 years, 2 months ago

I was a bit heated after getting the question wrong, sorry if I came across as contentious. You got it exactly right, when answering the question "what species are incompatible with B" I went to the table under the B row and got an answer: E and I. It did not occur to me to then search through the entire table to see if entry B might have been in one of the other rows for the other species. This has not been my experience with other index/lookup articles. Of course I should have been more thorough.

Vadim Evstifeev - 3 years, 2 months ago

@Vadim Evstifeev – No worries. I've been a bit startled too...I've thought about putting all species compatibility into a matrix but it felt too busy on the screen. Anyways thanks again.

Romain Bouchard - 3 years, 2 months ago

Nothing Fishy

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