Question: If two of them wear the same colour, then how many of the following must be false?
I. Amar wears blue and Akbar does not wear green
II. Amar does not wear blue and Akbar wears blue
III. Amar does not wear blue and Akbar does not wear blue
IV. Amar wears green, Akbar does not wear red, Anthony does not wear green
If two of them wear the same colour, the following six combinations will exist: since Amar does not wear red, he can either wear blue or green. In either case, the remaining two will have to wear red, Akbar does not wear green, and Anthony does not wear blue. This gives the combinations 1 and 2 below. Similarly, the other combinations can be worked out.
Using this we can evaluate the statements. (I) is true as we can see that in all the cases, if Amar wears blue, Akbar does not wear green. (II) needs not be false always, as in combination 4, we can see that Amar does not wear blue but Akbar wears blue. (III) is also not necessarily false as in combinations 1 and 3, both Amar and Akbar do not wear blue. Statement (IV) is necessarily false since if Amar wears green and Akbar does not wear red, then combination 4 is the only combination possible and hence Anthony should wear green. So only one of the four statements must always be false.