Algernon, Basil and Clarence
are either English or Irish, either
Conservative or Liberal, and either
Protestant or Catholic. In each case
there is, as they all know, at least
one of each.
None of them know which the
others are, but Algernon and Basil
have both been told that if Clarence
is an Irish Catholic he cannot be a
Liberal.
Basil asks Algernon whether he is a Conservative or a Liberal,
and whether he is English or Irish.
Algernon tells him.
After a pause for reflection, Basil
is able to announce correctly the
full particulars (English or Irish,
Protestant or Catholic, Conservative
or Liberal) of both Algernon and
Clarence.
Determine the particulars for the
three men.
Suppose Algernon tells Basil he's Conservative. If Basil is Liberal, then Clarence could be of either persuasion, so Basil couldn't know his particulars. But if Basil shares Algernon's Conservative bent, he knows Clarence must be Liberal or there wouldn't be one of each.
Since Basil knows everyone's particulars, Algernon and Bail must match on English/Irish and on Conservative/Liberal, and Clarence must be opposite on both.
Now, they also know that Clarence cannot be an Irish Catholic Liberal.
Suppose Algernon & Bail are both English and Liberal. Then Clarence is Irish and Conservative, and could be either Catholic or Protestant without violating the extra constraint. Ditto if Algernon and Basil are both Irish (and any political persuasion). But if Algernon & Bail are both English and Conservative then Clarence is Irish and Liberal and MUST be Protestant, because he can't be both and Irish Catholic and Liberal.
Since only this case allows Basil to arrive at a solution, that's the case that must have occurred. Algernon and Basil are both English and Conservative, and Clarence is Irish, Liberal, and Protestant.
Finally, Basil certainly knows his own religion, but if he were Catholic, then Algernon could be either Catholic or Protestant. Since he deduces Algernon's religion, it must be that Basil is Protestant, and Algernon is the sole Catholic representative of the three.
So:
Algernon = English, Catholic, Conservative
Basil = English, Protestant, Conservative
Clarence = Irish, Protestant, Liberal
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Posted by Paul
on 2024-12-08 12:53:27 |
Solution
