## Village of Perfect Reasoning

A forum for good logic/math puzzles.

Moderators: jestingrabbit, Moderators General, Prelates

Gyvulys624
Posts: 35
Joined: Tue Oct 16, 2007 9:49 pm UTC

### Village of Perfect Reasoning

I did a search and didn't find this one here Someone already answered it before I could on my other forum, but he didn't explain it well enough to my liking, or understanding. So please give a crack at it.

In the village of Perfect Reasoning, each employer has an apprentice. At least one apprentice is a thief. To remedy this without embarrassment, the mayor proclaims the following true statements: "At least one apprentice in this town is a thief. Every thief is known to be a thief by everyone except his or her employer, and all employers reason perfectly. If n days from now you have concluded that your apprentice is a thief, you will come to the village square at noon that day to denounce your apprentice." The villagers gather at noon everyday thereafter. If in fact k>=1 of the apprentices are thieves, when will they be denounced, and how do their employers reason?

Again, I'm looking for an answer and a well explained proof.

Buttons
Posts: 858
Joined: Wed May 02, 2007 3:27 pm UTC
Location: Somerville

### Re: Village of Perfect Reasoning

Spoiler:
Well, everyone knows that thieves only steal from employers with blue eyes. If an employer sees that there are k other employers with thieves, and that said employers don't show up after k days, then that employer will show up on the k+1-st day to proclaim that his apprentice is a thief. That is, if there are n thieves total, then all of the blue-eyed people will leave the island after n days after the guru speaks.
Or something like that. I may have been mixing up my problems.

(Less cheekily: there's already a thread on this, but it's worded differently.)

DrStalker
Posts: 271
Joined: Thu Aug 30, 2007 8:15 am UTC
Location: Sydney

### Re: Village of Perfect Reasoning

There's also the version where some husbands are unfaithful and every wife (except the cheaters own wives) know they are. And the monastery where blue-eyed monks have to throw themselves off a cliff, but they can't talk to tell each other what eye colour they have.

When you know a puzzle like Blue Eyes it's very easy to look at something like this and say "it's just Blue Eyes, worded differently" but if you don't know the puzzle good luck ever finding Blue Eyes from this. If only the forum search allowed us to search for the logical concepts in problems instead of text.

Token
Posts: 1481
Joined: Fri Dec 01, 2006 5:07 pm UTC
Location: London

### Re: Village of Perfect Reasoning

DrStalker wrote:There's also the version where some husbands are unfaithful and every wife (except the cheaters own wives) know they are. And the monastery where blue-eyed monks have to throw themselves off a cliff, but they can't talk to tell each other what eye colour they have.

When you know a puzzle like Blue Eyes it's very easy to look at something like this and say "it's just Blue Eyes, worded differently" but if you don't know the puzzle good luck ever finding Blue Eyes from this. If only the forum search allowed us to search for the logical concepts in problems instead of text.

Hmm... I wonder if Google will ever come up with an algorithm for that?
All posts are works in progress. If I posted something within the last hour, chances are I'm still editing it.

DrStalker
Posts: 271
Joined: Thu Aug 30, 2007 8:15 am UTC
Location: Sydney

### Re: Village of Perfect Reasoning

Token wrote:Hmm... I wonder if Google will ever come up with an algorithm for that?

If I was going to bet on who would design such a thing eventually I'd wager on Google.
There are two types of people in the world: 1) those that can extrapolate from incomplete data.

Gyvulys624
Posts: 35
Joined: Tue Oct 16, 2007 9:49 pm UTC

### Re: Village of Perfect Reasoning

Maybe someone already started. But they will probably learn to levitate - many times - before it is implemented. (Trusting you guys all know the comics round here - I spent hours on Friday going through them all - around number 250 I realized there were those roll over comments too, so I went back again).

Basil
Posts: 1
Joined: Mon Oct 22, 2007 6:52 am UTC

### Re: Village of Perfect Reasoning

Spoiler:
k

There is at least 1 thief.
Every thief is known by everyone except their employer.

If the employer knows of no thieves, their apprentice must be it.

For example, if there are no thieves announced on the first 2 days, three employers will step forward, because they each only know of two thieves, their own apprentice must be a thief. On the third day each announces their discovery.