Puzzle 3: No Honesty Amongst Thieves

Lucas Bachmann

The solution to the previous puzzle can be found here.

If you’ve missed any of the story so far, you can catch up on all of the puzzles here.

“So these bills are counterfeit!” decried Hansel “I would have never guessed it”

“Yes, Constable”. Bernoulli pondered for a bit. What was the point of swapping real bills for counterfeits? It seems like extra work for very little gain. In addition, there was no sign of forced entry, which means the intruders probably had some key or access to the bank, which can only mean…

“Constable, this might have been an inside job. The thieves work in the bank, and planned on swapping real money out for fakes. Since they are familiar with the layout of the building, they would know how to avoid security cameras, and getting access is child’s play. Furthermore, nobody would be none the wiser, and they would be able to pull this crime off multiple times, if they hadn’t been caught.”

“So you suspect the staff to be involved in this matter?” asked Hansel

“Yes, we should interrogate them as soon as possible”. Hansel and Bernoulli headed upstairs. The police had already gathered some of the employees into one of the offices. One of the officers approached Hansel, and with nervousness, spoke

“Sir, we’ve interviewed all of the staff in this bank. However, their testimony… they are all pointing fingers at each other!”

“Don’t worry”, Bernoulli stated, “We’ll sort this out soon enough.”

“Let’s start with a simple enough premise. If the interviewee is a thief, then he has a good incentive to point the finger at somebody else, and thus is lying. If the interviewee is not a thief, then they do not have an incentive to lie. From this, let us figure out who must be lying, and who must be telling the truth.”

Statements from suspects:

Jane: I definitely saw Pierre hide something in his desk last night. He must have something to do with it!

Pierre: I swear I was at home watching TV all evening. I am not a thief!

Frank: George and Christina are always together. I wouldn’t be surprised if both of them committed this crime.

George: I took the same bus as Jane last night. I know she didn’t do it.

Christina: I was leaving when I saw a suspicious black-haired individual hanging near the entrance to the vault. I suppose that since Frank and George both have black hair, either of them could be a thief.

So, who’s lying?

Scroll down to reveal the solution.

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Solution

Bernoulli ponders for a minute, then smiles and turns to the Constable:

“I think I know who the thieves are. Let me explain my reasoning.”

“First, let’s assume Frank is telling the truth, that both Christina and George are thieves. Then, Christina would be lying, which would imply neither George nor Frank was a thief. But since George cannot be both a thief and not a thief, we have a problem. Thus, our original assumption is wrong, which means Frank is lying, and thus a thief. This also means Christina’s statement is true, thus she is innocent.”

“And now, all of the dominoes collapse: Pierre claimed he was with Frank at home when Frank was clearly at the Bank, thus Pierre is also a thief. Jane was right to suspect Pierre, so she’s innocent. George’s statement also reaffirms Jane’s innocence, thus he must also be innocent.”

“Therefore, I can now conclude that Frank and Pierre are our two thieves! Arrest them!”

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