Alice goes to an office to collect form A. There are exactly 5 kinds of forms available at this office, forms A, B, C, D and E.
Also, there are 5 terminals at the office and each terminal provides a different kind of form. For example, if form C is available at Terminal 2, then no other terminal will have form C.
Each terminal has a sign board. Here's what's written on the various sign boards:
Terminal 1: “Form B is available here.”
Terminal 2: “Form C or E is available here.”
Terminal 3: “Form D is available here.”
Terminal 4: “Form A, C or E is available here.”
Terminal 5: “Form A is available here.”
Alice suddenly remembers what a friend of hers told her, "Exactly one sign on the terminals is wrong, the other four signs are right."
After remembering her friend's statement. Alice goes to the right terminal. Which terminal did Alice go to?
Difficulty rating:
Easy, 4/10
Solution
Terminal 1: Let's assume that the sign at Terminal 1 is false and all the others are true. But if this is the case, then form B won't be available at Terminal 1 and, at the same time, it won't be available at one of the other terminals either.
But form B has to be present at one of the terminals because there are 5 terminals, 5 forms and each kind of form is available at a different terminal.
So, Terminal 1's sign cannot be false. This means that Terminal 1's sign is true and form B is available there.
Terminal 2: Let's assume that the sign sign here is false and all the other signs are true. Then this terminal has form A or D.
But then at least one of statements 3 and 5 becomes false which is a contradiction. So, this statement has to be true.
Terminal 3: Now, let's assume that this sign is the one that's false. If this was the case, then all the other signs would be true and form D won't be available at any of the other terminals. But each kind of form has to be available at some terminal. So, this sign cannot be false either.
Terminal 4: If this statement was false then the form B or D would be available here. However, we already know by now that B and D are at terminals 1 and 3 respectively. So, this statement has to be true.
Terminal 5: Since we have shown that all the above statements are true, it implies that this statement is false. This means that form A is available at terminal 4. So, Alice went to Terminal 4.