Find the spy anyway

Logic Level pending

In a high-security facility there is searched the identity of a spy. It's known that the spy is one of the 3 new employees anyway : B , A , D.

They are together taken at an interview whose results are given bellow. The comitee who sustains the interview is able to find therefore the following things.

A. 1. I' m sure the spy is D. 2. The first statement of B is true anyway.

B. 1. I am not a spy. 2. The spy is A anyway.

D. 1.The second statement of A is true anyway. 2. But the second statement of B is false.

The investigation comitee only knows the spy made one true and one false statement but doesn't know anything about the truth of the other statements.

Who is the spy anyway ?

He can't be determined anyway A anyway D anyway B anyway

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2 solutions

Afkar Aulia
Aug 16, 2016

There are only 3 different Cases: If A is spy, then his first statement is false while his second statement is correct (still fitting the description of spy) If b is spy, both of his statement is wrong (contradictory with the nature of spy) If d is spy, both of his statement is correct (contradictory with the nature of spy)

so the spy is A

Btw, the usage of the word anyway sounds off

That's a pretty good non-detailed reasoning.

I know the word "anyway"sounds off ,thanks for posting a solution btw Afkar Aulia.

A A - 4 years, 10 months ago

................................................................................anyway

NSCS 747 - 11 months, 1 week ago
Saya Suka
Feb 8, 2021

I'm sure that by using assumptions, we can get to the answer faster, but that kind of reasoning has already been posted as a solution before, so I'll try another approach without the "what ifs".

Statements by A
1) I' m sure the spy is D.
2) The first statement of B is true anyway.

Statements by B
1) I am not a spy.
2) The spy is A anyway.

Statements by D
1) The second statement of A is true anyway.
2) But the second statement of B is false.

In essence, all three of them mentioned something in a unified voice of B's innocence with B's "I'm not a spy", A seconding the motion and D agreeing with A. We don't know if this mutual understanding is really the truth or not, so let's see what other things that B, A and D were saying.

Other than their informal pact, B was actually accusing A, while A turned around and accused D instead and D, bless their kind soul, reacted by denying B's accusation of A in a selfless act of defending his accuser.

We were only told that the real spy stated both the truth and a lie, one of each, so we have to find something that is opposite in the truth value of their mutual pact. A true pact would have the spy to accuse another innocent party or defend themselves as the guilty spy while a spy stating a false mutual agreement would have to accuse themselves (admitting to the industrial espionage crime) or defend an innocent co-worker.

Since we haven't seen any suspect accused themselves, ever, nor defended themselves outside of the pact, then the spy must either have accused an innocent co-worker alongside the true mutual pact or defended an innocent party all the while still maintaining the innocence of their guilty self (by that false mutual pact).

In conclusion, the spy MUST defend one of the other AND do either one of these two things : accuse the other innocent party OR defend themselves. With D being all altruistic by defending everyone else but not themselves (a proper spy would defend both parties, their guilty self & an innocent other, OR defend one innocent while accusing another) and B who was too selfish to at least fake an act like they care about others (B did both the spy optional moves, but didn't complete the mandatory one), we are left with spy A anyway.

{ These below are in depth analysis for why D & A cannot be a spy, if the last paragraph above with the conclusions seemed too rushed for your taste. The 2 should explain clearly the why of the impossibilities, one step at a time to substitute the above conclusive paragraph. }

Now, with D being the only suspect among the three who defended another person had never said anything about their (D's) innocence themselves, then we know that D cannot be a spy because D didn't do things the way a spy would and should do, as we have analysed in the previous paragraph (a spy who defended others MUST also do something to defend themselves -- either by a direct self-defence or accusing another as a deflection tactics -- to balance their true defensive statement of an innocent co-worker with a lie about their own or the third person's innocence).

Conversely, with B being the only suspect among the three who said anything about their (B's) own innocence did not defend any other than themselves, then we know that B cannot be a spy because B didn't do things the way a spy would and should do, as we have analysed in a previous paragraph (a spy who defended themselves MUST also defend others, to balance their lie about their own innocence with a true defensive statement of an innocent co-worker).

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