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Alice and Bob are supposed to get form A at the joke office.

Forms A, B, C, D and E are each at exactly one of the following five terminals. At one Terminal is only one form.

Terminal 1: Here there are form B.

Terminal 2: Here there are form C or E.

Terminal 3: Here there are form D.

Terminal 4: Here there are form A, C or E.

Terminal 5: Here there are form A.

Bob is ​​at a loss when he reads the signs at the counters.

Alice remembers what the janitor is said: "Exactly one statement on the terminals is wrong, the four other statements are true."

Question:

At which terminal is form A available?

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    $\begingroup$ Is switch the right word, or were you looking for "counter" or "terminal" ? $\endgroup$ – Falco Jul 9 '19 at 11:20
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    $\begingroup$ Yes, terminal is better. $\endgroup$ – Matti Jul 9 '19 at 11:32
  • $\begingroup$ You should specify that at each terminal there is exactly one form, otherwise there are alternate solutions, for example with B at 1, C and E at 2, D at 3 and A at 5. $\endgroup$ – Magma Jul 9 '19 at 14:03
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Notation: (P,Q,R,S,T) denotes that form P is in Switch 1, Q in Switch 2, etc.

If Switch 1 is wrong, then

(?,C/E,D,C/E,A), only choice left for ? is B -> contradiction

If Switch 2 is wrong, then

(B,?,D,C/E,A), only choices left for ? are C and E -> contradiction

If Switch 3 is wrong, then

(B,C/E,?,C/E,A), only choice left for ? is D -> contradiction

If Switch 4 is wrong, then

(B,C/E,D,?,A), only choices left for ? are C and E -> contradiction

If Switch 5 is wrong, then

(B,C/E,D,A/C/E,?), one scenario can be (B,C/E,D,A,C/E) -> possible

Answer

Form A: Switch 4; Wrong Sign: Switch 5

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Form A is available at

Switch 4.

Assume

Switch 1 was incorrect. This means that form B must be somewhere else. But there is no other sign which references form B, so that would mean more than one sign was incorrect (contradiction!). If we assume Switch 3 was incorrect, we’d get the same result. So one of Switches 2, 4, or 5 are wrong. It can’t be 4, because then B or D would have to be there too and those have already been placed. Assuming that Switch 2 was wrong would put A at Switch 2, but then Switch 5 would also be wrong. Therefore Switch 5 must be wrong, so all of the others are right, and since Switch 4 is the only place with mention to A, it must be there.

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    $\begingroup$ you sniped me with only the answer, but i have the full explanation first. let the judge decide! good game! $\endgroup$ – Omega Krypton Jul 8 '19 at 12:24
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Let us assume for contradiction sake Switch 5 was correct. If Switch 1 and 3 are correct only C and E are left for Switches 2 and 4 which would thus be correct, too. Similarly if Switches 2 and 4 are correct only B and D are left for Switch 1 and 3 and either both or none of them is correct. Thus, there is no way that Switch 5 is correct and exactly one of the remaining switches incorrect. This implies that Switch 5 must be the incorrect one. The only Switch remaining which could possibly contain Form A is Switch 4.

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  • $\begingroup$ Hi! Welcome to the Puzzling Stack Exchange (PSE)! Great job on your first answer! I'm glad you have learnt to use the spoiler tag >! and have even answered the question correctly — and pretty nicely too with a thorough explanation! — so well done! Take the tour if you have not already, just to get a clearer understanding of what this site is all about, as well as the community thriving on it. Also, check out the Help Center to know how you may contribute to this community. Apart from that, enjoy! :) $\endgroup$ – Mr Pie Jul 9 '19 at 9:57
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Terminal 4 is wrong as it must contain either Forms C or E, thusly Bob should go to Terminal 5 to retrieve Form A

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