Puzzle: The Candy Thief


#1

Originally published at: http://boingboing.net/2017/03/09/puzzle-the-candy-thief.html


#2

I’m still trying to figure out who stole the kishka…


#3

My solution:

[spoiler]All right, let’s start off with Dennis:

Dennis:
10. I didn’t take the box of candy. 11. Linda did it. 12. Ivan is lying when he says I stole the candy.

#10. and #12. are identical in meaning, so either both have to be true, or neither is true. Since each child is telling two truths and one falsehood, that means neither Dennis nor Linda took the candy.

Now, to Ivan:
1. I didn’t take the box of candy. 2. I have never stolen anything. 3. Dennis did it.

#3, we already know is false. Therefore, #1 and #2 are true, and Ivan did not steal the candy.

Next, Ernie:
7. I didn’t take the box of candy. 8. I didn’t know Linda until this year. 9. Dennis did it.

Again, #3, we already know is false. Therefore, #1 and #2 are true, and Ernie did not steal the candy.

Now, four of the five kids have been eliminated. Sylvia is the only remaining suspect.

Let’s examine Sylvia’s statements:
4. I didn’t take the box of candy. 5. I’m rich and I can buy my own candy. 6. Linda knows who the crook is.

If the first statement is false, and the second (which has nothing to do with whether she did take the candy, only one motive she might have for doing so) can easily be true regardless of her guilt or innocence, then, to be telling two truths and a lie, she can be guilty if and only if Linda knows that she did it.

So, finally, what does Linda have to say?:
13. I didn’t take the box of candy. 14. Sylvia is guilty. 15. Ernie can vouch for me, because he has known me since I was a baby eight years ago.

#15 is directly contradicted by #8, and we already know #8 is true. Therefore, #15 is false, #14 is true, and Linda is accusing Sylvia, which confirms both #13 and #6.

Sylvia is your culprit.
[/spoiler]


#4

Silvia. I didn’t really figure it out smart like, I just had my suspicions about her from the start, plugged that in and it worked


#5

I really like this puzzle. It’s actually a logic puzzle, and there is a twist, but it’s a completely fair twist that tries to play on people’s assumptions.


#6

Do you mean how two people are accusing Dennis, so he looks guilty?


#7

I recalled that the last time I saw a similar problem (albeit a considerably simpler one) that the culprit was the one who wasn’t trying to accuse someone else of either stealing or lying. Still works here.


#8

I meant that Sylvia appears to deny stealing the candy twice, but her second denial isn’t really a denial, it’s a reason we might think she didn’t do it..


#9

Cary:


#10

Hmm. Actually her second statement had the opposite effect for me because of the obnoxious attitude; I immediately thought “I’m taking you down, asshole”.


#11

Yeah, me too. I still appreciated it that it was true but not exculpatory.


#12

The difference is that if she’d turned out to be innocent, I would have doctored the evidence to make sure she got the chair.


#13

I’m not saying, but it rhymes with “Pulverine”.


#14

So the real solution is “destroy the evidence”.


#15

This one only looks complicated, people are overthinking it.

[spoiler]Any kid who says both “I didn’t do it” and “so-and-so did it” can’t be the thief, because if “I didn’t do it” was the lie, then so-and-so would also have to be the thief.

Every kid but Sylvia says some version of this. So it has to be Sylvia.

It’s entertaining to trace the rest of the statements out, but unnecessary to solve the puzzle.[/spoiler]


#16

The candy theft was a false-flag operation to distract from the unanswered electrician puzzle. What’s the deal, Frauenfelder?


#17

My main conclusion: what a terrible bunch most of those kids are. Ivan, Ernie, Dennis I’m looking at you - bearing false witness against others like it was nothing.

If they were friends before, this is going to be the end of it.


#18

Very elegant.


#19

What makes you think each child made two true and one false statement? This is not how children work. I say the AI did it.


#20

True, but not methodical. It presumes that the problem can be solved, and doesn’t rule out the possibility of an poorly-constructed puzzle where no solution will meet all of the criteria.

Admittedly, you can use the shortened process to come up with the correct solution, and then verify each of the statements individually, but where’s the fun in that?