So I sent him this:
The following assumes that Walter is an intelligent, rational being.
Now, what would he reply to each statement? Let's go through each case, if he's a truthteller (T), a liar (F), or a spy who can choose to lie or not whenever he wanted (S):
Statement 1: If I were to ask you "are you working for The Order?" you would deny it.
T: If he was with the order he'd be truthful and wouldn't deny it, so the statement is false and he would truthfully reply "statement 1 is false." If he was against the order he would rigthfully deny my accusation, the statement is true, and he would truthfully reply "statement 1 is true." Thus, we can deduce his allegiance to the order from his answer: true=anti-order, false=pro-order
F: If he was with the order he would lie and deny it so my statement is true, but he would lie in his reply and send, "statement 1 is false." If he was against the order he would lie and pretend to admit that he was pro-order when he really wasn't and the statement would thus be false, but he would reply back with a lie: "statement 1 is true." We can deduce his allegiance to the order from his answer. true=anti-order, false=pro-order.
S: The statemet is false because he could freely choose whether to deny my accusation or not. So, the only question is whether he wants to reply truthfully or not. true=he lied false=truthful
Statement 2: You're just like me (see above) XOR your answer to this statement will be a lie.
From the introduction about myself, I obviously can't be a truthteller, and I can't be a liar either (the statement would be true, a contradiction). Thus, I am a spy (can choose to lie or not whenever I want, and I chose to lie on that one).
T: He's not a spy like me, and he can't lie, so the XOR statement is false. He would truthfully reply "statement 2 is false."
F: He's not a spy like me either, and his answer will be a lie, so the statement is true. He would lie in his reply and say "statement 2 is false."
S: He's a spy like me, and he can decide to lie or not in his answer. If he answers truthfully, the XOR statement is true and his reply would be "statement 2 is true." If he decides to lie, both sides of the XOR would be true, making the XOR false, and his lie for an answer would also have to be "statement 2 is true."
So, if he decides to reply, and he wants to be logically coherent, we can deduce the following:
1. true 2. true = he's a spy and lied on the first answer
1. true 2. false = he's anti-order but not a spy (either a liar or truthteller)
1. false 2. true = he's a spy and told the truth on the first answer
1. false 2. false = he's pro-order but not a spy (either a liar or truthteller)
I suspect he'd go with the 3rd option, as that's the one that gives away the least and still allows for him to be truthful.
Just thought it would be fun to try it
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