Whom to trust?
As a spy, James Bond has 2 informants that submit tips anonymously. He knows that one of them has completely trustworthy information, but the other is not always perfectly accurate. He asked them to figure out if statements W, X, Y, Z, and received the following reports:
Report A:
Exactly one of W, X, Y is true.
Exactly one of X, Y, Z is true.
Exactly one of W, Z is false.
Report B:
Exactly one of W, X, Y is true.
Exactly one of X, Y, Z is true.
Exactly one of W, Y, Z is true.
Which report is NOT trustworthy?
This section requires Javascript.
You are seeing this because something didn't load right. We suggest you, (a) try
refreshing the page, (b) enabling javascript if it is disabled on your browser and,
finally, (c)
loading the
non-javascript version of this page
. We're sorry about the hassle.
1 solution
Moderator note:
Clearly presented solution.
Thanks for also demonstrating that there is a set of truth values to the statements which satisfy the conditions of the problem.
Since both spies have the same first two statements and one of them is trustworthy, those statements MUST be true.
Therefore:
(I) Exactly one of W, X, Y is true.
(II) Exactly one of X, Y, Z is true.
If either one of X or Y is true, then W is false by (I) and Z is false by (II).
If both X and Y are false, than W is true by (I) and Z is true by (II).
Therefore, W and Z are either both true or both false.
Spy A stated that EXACTLY ONE of W and Z is false. This is impossible. So A is the untrustworthy spy.
(Incidentally, since B is trustworthy, exactly one of W, Y, Z is true, which makes W, X.and Z false and Y true.)