Knights and Knaves in Slylock Fox

Oh look! A knights and knaves puzzle in a low rent kid’s funny papers strip. Can we solve this puzzle with the method of Raymond Smullyan’s Og and Bog problem? Let’s find out.

I see three statements made by the 3 Great Apes in the line up, Larry, Moe and Curly (left to right).

1. Moe can say “Moe took it”.
2. Larry can say “Moe took it”.
3. Curly can say “Moe or Larry didn’t take it”

Just like in my Og and Bog post, I’ll collapse some English phrases into short symbols.

• Kx will mean “x is a knight”, so KM will mean “Moe is a knight”, who always tells the truth.
• Tx will mean “x took the truckload of bananas”. TL will mean “Larry took the truckload of bananas”.

I collapse the 3 statements into symbols like this:

1. KM = TM
2. KL = TM
3. KC = ~(TM | TL)

This follows the logic of: if someone is a knight, and they can say something, it’s true, but if someone is a knave and they can say something, it’s false. Logical equivalence.

My symbolic 3rd statement is different than how Smullyan would translate “Moe or Larry didn’t take it”. I cheated and read Bob Weber’s “solution”. Weber clearly interpreted Curly’s statement this way.

Just for completeness’ sake, there’s 5 logical variables, KM, KL and KC, TM and TL

KC	KL	KM	TL	TM	((KM = TM) & (KL = TM)) & (KC = ~(TM | TL))
true	true	true	true	true	false
true	true	true	true	false	false
true	true	true	false	true	false
true	true	true	false	false	false
true	true	false	true	true	false
true	true	false	true	false	false
true	true	false	false	true	false
true	true	false	false	false	false
true	false	true	true	true	false
true	false	true	true	false	false
true	false	true	false	true	false
true	false	true	false	false	false
true	false	false	true	true	false
true	false	false	true	false	false
true	false	false	false	true	false
true	false	false	false	false	true
false	true	true	true	true	true
false	true	true	true	false	false
false	true	true	false	true	true
false	true	true	false	false	false
false	true	false	true	true	false
false	true	false	true	false	false
false	true	false	false	true	false
false	true	false	false	false	false
false	false	true	true	true	false
false	false	true	true	false	false
false	false	true	false	true	false
false	false	true	false	false	false
false	false	false	true	true	false
false	false	false	true	false	true
false	false	false	false	true	false
false	false	false	false	false	false

Wow, 4 true statements. One where Moe took the truckload of bananas, one where Larry took the truckload of bananas, one where Moe and Larry took it, and one where neither of them took it. Got all the banana truck thievery bases covered.

Looks like if Slylock Fox the comic strip took place on the Island of Knights and Knaves, Bob Weber posed an ill-formed problem.

If you stand on your head and read Weber’s “solution”, you find that you are supposed to assume Larry, Curly and Moe are knaves. This is implicit in Weber’s “logically negate all 3 statements, then assume they’re true”.

Logically negate (“the opposite”) of each statement:

1. “Moe didn’t take it” → ~TM
2. “Moe didn’t take it” → ~TM
3. “Moe or Larry took it” → (TM | TL)

This 3rd statement is where Weber’s non-standard interpretation shows up.

The truth table for a conjunction of these 3 statements:

TL	TM	~TM & ~TM & (TM | TL)
true	true	false
true	false	true
false	true	false
false	false	false

That works out as Weber claims. However…

If Larry, Curly and Moe all lied, then Larry took the truckload of bananas. This seems like an unwarranted assumption. If one of Larry, Curly or Moe actually stole the truckload of bananas, sure, the miscreant would lie about it to avoid a conviction, but then the other two should tell the truth and say who actually did steal it.

This is just a bad puzzle.

I discovered this dumbass puzzle on the Comics Curmudgeon blog. You should read Comics Curmudgeon. It’s a lot funnier than the “funny pages”, and contrary to Internet Tradition, the commentors are both topical and funny.