[Freddy]

Can there be three red dots ?

I'm stuck on what looks like two of them could work out their colour but only one came forward.

[Freddy]

My reasoning is this.

You need a minimum of two red dots for all three to tap.

If you can see one white dot and one red dot, then you know you must have a red dot.

But that's where I am stuck because it's possible for two of them to be in the same situation.

If all three tap and you see all reds, then there is no telling if you have white or red due to the minimum of two red dots needed to make them all tap.

[infurl]

Freddy you are really close. Here's a hint, you need tri-state logic not binary logic to solve this puzzle. That is TRUE, FALSE and UNKNOWN. You also need empathy to model what the others know or don't know.

[Freddy]

One coffee later.

If we take it from two being red and one unknown - which covers three red and also two red and one white.

The two reds know that only one can be let free, so as they both know they are red they cannot both be set free so don't go to the warden.

Time passes. The guy with the unknown sees that neither of the other two have left - therefore he knows they have worked out that they are both red.

The only way for them to work out they are both red is for them both to have seen a white dot - which leads him to realise he is the one with the white dot and off he goes to the warden.

[infurl]

Ah no, you're headed down the wrong track there.

It doesn't say only one can go free, it says anyone who knows the color of their dot can go free.

[Freddy]

To be honest I thought I was going off track. 

[Freddy]

Coming at it from a different angle.

Assuming these people do want to get out of jail !

Going with you need to see a red + white to know you are red which is the only certainty as all of them tapped.

Seeing two reds leads to an unknown - you don't know if you are red or white. And seeing white + white clearly did not happen as they all tapped.

The guy that left couldn't have had a white dot because the other two would have known that they are red for sure and surely would have got out.

Assuming the slight time delay is significant, is it just that one of them realised that no one knew anything for sure, meaning all were red. It's just he took the next step before the others.

So the guy that left had a red dot as he realised the uncertainty could only point to one thing.

[infurl]

You are one hundred percent correct Freddy.

The simplest way to describe the solution is with a truth table, and this is probably how you would program an AI to solve it.

There are three prisoners with two possible states each giving you 2^3=8 possible situations. Some of these are equivalent so the truth table reduces to this:

1. WWW
2. WWR
3. WRR
4. RRR

Since all three prisoners could see a red dot, you can eliminate cases 1 and 2. Add another column "Obvious Answer" to what's left of the truth table and you get this:

3. WRR-Y
4. RRR-N

Since none of the prisoners could work out the answer immediately it must have been 4 and the prisoner had a red dot.

The lesson here is that sometimes not knowing something is just as significant as what you do know.

(edited to fix a typo)

[Freddy]

  Nice. That was a really good puzzle 

I did do some similar scribbling here. For a while there I was stuck with the two reds and one white - I was looking at how the guy could have a white dot (as the other two were mirror images of each other and I couldn't derive anything form them). Then there was a little leap of faith.

It's been a while since I played with truth tables. Lesson learnt. 

[yotamarker]

that was my answer ! 

[yotamarker]

if your puzzle assumes a prisoner sees the other two at all time and the warden was there from the get
go


the few minutes suggests an uncertainty which would come from the all red narrative.

[infurl]

Sorry yotamarker I really thought hard about whether or not to give you credit but decided not to because, of your three assertions, the first two were quite wrong which suggested pretty strongly that you hadn't figured it out.

for the prisoner it is no problem just face one guy and know your color

1. Wrong because they are not allowed to communicate with each other.

for the solver if all 3 constantly tapped they are all red

2. Wrong because they could be all red or two red and one white for all three to be tapping on the floor.

the few minutes suggests an uncertainty which would come from the all red narrative

3. This would have amounted to a correct solution *iff* your second statement above had been correct.

Thanks for giving it a good try.

[LOCKSUIT]

Even after scrolling up and down this page a few times and reading different pieces of the text in everyone's replies I still don't understand the quiz little own fetching an answer.

If it's that confusing, it has nothing to do with AI.

But honestly, dependless of any task like AND AND OR BUT functions my system works with all of such things, so all we can do like that it can.

[Freddy]

If it's that confusing, it has nothing to do with AI.

  That made me laugh.

[yotamarker]

if she works as a detective she might need this puzzle skill