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## Question

Following the recent breakdown in diplomatic relations, the government of Honestants and Swindlecants is taking a hard line on foreigners, declaring all “Normaltons” (people who can tell the truth or lie at will) detrimental to the logical integrity of society. Yesterday I was backpacking on the island with a companion. The secret police found us and took us both to a detention centre. We were forcibly separated and I was locked in a solitary cell. That night I heard terrible screams, and in the morning there was an eerie silence. Fearing the worst, I called out my companion’s name, but there was no reply. There were two guards outside my cell so I asked them what had become of my companion.

Guard 1: “If your companion is dead, the other guard is an Honestant.”

Guard 2: “If the other guard is an Honestant, your companion is alive. Unfortunately, the other guard is a Swindlecant.”

That sounds like bad news, but is it really? Is my companion alive, or dead?

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First, let's see which guards are truthful.

From g2's 2nd statement, g1=g2=H and g1=g2=S are eliminated.

If g1=H, your companion is alive. Otherwise g1's inference makes g2=H as well.

If g2=S, your companion is dead. Invalid inference requires a true premise [-> g1=H] and false conclusion [-> comp is dead].

So g1=H contradicts g2=S, that combination is eliminated.

Thus g1=S and g2=H. Let's check this out.

g2=H makes his conclusion true [-> companion alive] OR his premise false [-> g1=S].

Since g2=H implies g1=S, the OR is satisfied for either state of the companion. That's consistent, but it gives no information about the companion.

g1=S makes g1's premise true [-> companion alive] and conclusion false [-> g2=S]. That's a contradiction.

There seems to be no self-consistent assignment of S and H for g1 and g2.

For an inference If A then B I use the truth values of ^A or B: if the premise is false or the conclusion is true, than the inference is true.

That is, an inference is false if and only if A is true and B is false.

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Let's consider the only two possibilities for Guard 1:

Possibility [1] Guard 1 Honestant:

(1) Friend dead AND Guard 2 Honestant [ If True then True = T]

(2) Or simply Friend alive [if False then X = T]

(1) ==> Guard 2 Honestant and his affirmation must be false

==> Guard 1 is a Swindlecant <== contradiction

(2) ==> Friend Alive

and Guard 2 affirmation becomes: If T then T = T He is a Honestant + F He is a Swindelcant (Contradiction)

[2] Guard 1 = Swindelcant:

(1) Friend Dead AND Guard 2 is Swindelcant [if False then True = F]

Guard 2's affirmation becomes:

The other Guard is a Swindelcant = T (contradiction)

We could have easilly reasonned out of the two possibilities:

[2] Friend Alive

But still, this doesn't mean there is no answer here!

The only answer I can figure out is that

GUARD 2 IS A NORMALTON AND MY FRIEND IS ALIVE!

Guard 1 = Honestant

Guard 2 = Normalton (first part of his affirmation = T and second part = F)

Friend = Alive

After all their society was infiltered by normaltons and apparently their secret police as well!

That's the only help I can provide here I supppose!

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Guard 1: “If your companion is dead, the other guard is an Honestant.”

Guard 2: “If the other guard is an Honestant, your companion is alive. Unfortunately, the other guard is a Swindlecant.”

possibilities:

A=alive

H=honestant

S=swindelcant

A-HH

A-HS

A-SH

A-SS

D-HH

D-HS

D-SH

D-SS

* take AHH, if they are both honestants, then both are lying. Cross AHH out

* take AHS, the first guy is telling the truth but then the second guy WOULDNT be lying. Cross AHS out

* take ASH, the first guy's statement works if the second guy is the honestant. But the second guy's first statement is a contradiction. Cross ASH out

* take a**, the first guy's statement only works if your companion dies, so this is already a contradiction. Cross a** out

we've eliminated all the alive possibilities

am I right?

just in case, I will look at the rest:

DHH- the second guy is lying, contradiction. Cross DHH out

DHS- this fits as far as I can tell

DSS- guard 2 is telling the truth, contradiction

leaving

DHS

guard 1: Honestant

guard 2: swindelcant

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wow it bleeped out A-S-S, ;D

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possibilities:

A=alive

H=honestant

S=swindelcant

A-HH

A-HS

A-SH

A-SS

D-HH

D-HS

D-SH

D-SS

* take AHH, if they are both honestants, then both are lying. Cross AHH out

* take AHS, the first guy is telling the truth but then the second guy WOULDNT be lying. Cross AHS out

* take ASH, the first guy's statement works if the second guy is the honestant. But the second guy's first statement is a contradiction. Cross ASH out

* take a**, the first guy's statement only works if your companion dies, so this is already a contradiction. Cross a** out

we've eliminated all the alive possibilities

am I right?

just in case, I will look at the rest:

DHH- the second guy is lying, contradiction. Cross DHH out

DHS- this fits as far as I can tell

DSS- guard 2 is telling the truth, contradiction

leaving

DHS

guard 1: Honestant

guard 2: swindelcant

H = Guard 1 Honestant

S = Guard 2 Swindlecant

But Guard 1 lied in that scenario:

If Friend dead (True) then Guard 2 Honestant (False) = False

So he cannot be a Honestant!

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I like roolstar's answer to this!

Not the right answer though, they haven't been infiltrated. Not yet anyway. Might use that later, hmm...

"How often have I said to you that when you have eliminated the impossible, whatever remains, however improbable, must be the truth?" - Sherlock Holmes

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i say alive

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guard2 is a swindlecant and guard1 is an honestant making guard 1s state ment true bu since guard 2 ix not an honestant he must be alive

but thier are probably other answers

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check out my puzzle

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Since this is only a little brainteaser, I'll post the answer now. Here it is...

No.

In case a little more detail is required...

If Guard 1 is a Swindlecant, his statement implies that Guard 2 is also a Swindlecant, but Guard 2’s second statement would be true (a contradiction).

So Guard 1 is an Honestant.

Guard 2's second statement shows that Guard 2 is a Swindlecant.

So what of my unfortunate companion?

Guard 1's statement can only hold true if my companion is not dead.

Guard 2's first statement can only be false if my companion is not alive.

Hence the answer, "No" (my companion is not "dead, or alive"). Which comes as no surprise considering the fact that my companion is a teddy bear. Did I forget to mention that?

Much respect to roolstar whose answer is every bit as valid as my own, being similarly based on overturning an unspoken assumption. Apologies to anyone who feels that such underhand trickery is against the spirit of Honestant-and-Swindlecantry. In my defence I thought the Sherlock Holmes hint (himself being neither alive nor dead) would have surely given it away. Anyway, I have another big H&S bubbling away in the pot, and rest assured I won't be resorting to such slipperyness next time!

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