17. Ali, Bev and Chaz never tell the truth. Each of them owns exactly one coloured stone that is either red or green. Ali says, "My stone is the same colour as Bev's". Bev says, "My stone is the same colour as Chaz's". Chaz says, "Exactly two of us own red stones". Which of the following statements is true?
A Ali's stone is green
B Bev's stone is green
C Chaz's stone is red
D Ali's stone and Chaz's stone are different colours
E None of the statements $\mathrm{A}$ to $\mathrm{D}$ are true
Solution
A

The question tells us that none of the three people tell the truth. Ali says that his stone is the same colour as Bev's and so we can deduce that Ali and Bev own different coloured stones and hence that there is at least one stone of each colour. Bev says that her stone is the same colour as Chaz's and so we can deduce that Bev and Chaz own different coloured stones and also that Ali and Chaz own the same coloured stones. Chaz says that exactly two of the stones are red and so we can deduce that Chaz and Ali own green stones and that Bev owns a red stone.
Hence only statement $\mathrm{A}$ is correct.