P, Q, R, and S are four brothers who went to an ice cream parlour. Each of them ate a different number of ice creams among 1, 2, 3, and 4. Since their mother do not allow more than one ice cream per day, they decided to report distorted information to her. So, each one of them decided to be a truth-teller, or a liar, or an alternator. Truth-tellers always tell the truth and liars always make false statements. Alternators, however, alternate between making true and false statements, in any order. Among the four, there is at least one truth teller, one liar, and one alternator. Each of the four brothers make the following statements –
P:
(i) The difference between the number of ice creams eaten by me and that by R is two.
(ii) S is not a liar.
Q:
(i) Exactly two of us tell the truth.
(ii) R ate one ice cream while P ate 3 ice creams.
R:
(i) Only one of us is an alternator.
(ii) S ate four ice creams.
S:
(i) I am an alternator
(ii) Only one of us is a liar.
Question 51
Who ate the most number of ice creams?