OH NO, firemonkey has been kidnapped!!!

[Sisyphus]

The evil king Sisyphus (no relation) kidnaps the handsome hero firemonkey and his equally heroic cousin powdermonkey and takes them to his far away kingdom.



He incarcerates them incommunicado in two separate rooms in his evil tower. The rooms each have one window that looks out over the kingdom. Before closing the doors they are told that they will be released if they can say how many villages there are in the kingdom.



Each day the jailer will visit them and ask how many villages there are. If they choose to answer it must be correct or they will be executed in such a manner that they will probably not risk guessing.



Because king Sisyphus is not irredeemably evil he does tell them that there are either ten or thirteen villages and that between them they can see all the villages.



Our handsome hero looks out, sees four villages, and draws up a cunning plan.



Sure enough the plan works and he is the one that confidently tells the jailer the correct answer.



How did he do it? And for a bonus point, how many villages are there?


Please spoiler your answers so as not to spoil things for others. Thanks.

I saw this quite a few years ago and I enjoyed it. I think I remember it correctly, sort of.

[genovese]

For the emoji use alone

The forum could do with a daily quiz, give the grey cells some exercise!

This question is beyond me tho

[Sisyphus]

I don't think I could do one like that every day, my brain would expolde.

Like most puzzles this one is easier than it looks. Not that that is any recommendation because it looks impossible at first glance.

Looking on the positive side, the harder they are the bigger the buzz when you get that AHA!! moment.

Don't just yet.

[Marco]

Good puzzle Sisyphus. I gave it a go, but I assumed that Firemonkey and Powdermonkey couldn't see the same villages to get my answer, so I might be well off the mark lol.

I think the answer is 10.

Let’s assume that both Firemonkey and Powdermonkey are equally smart and I’m also going to assume that neither of them can see any of the villages the other can see. Firemonkey knows therefore that Powdermonkey must be able to see either 6 or 9 villages.

Looking at this from Powdermonkey’s perspective, supposing Powdermonkey can see 9 villages, then firstly he can deduce that Firemonkey is able to see either 1 or 4 villages (we know he can see 4 of course). However, Powdermonkey will also be aware that since he himself is presently unable to answer, and if Firemonkey were only seeing one village, then Firemonkey would quickly be able to deduce that Powdermonkey’s silence gives away that he cannot see 12 villages (ruling out 13 villages), and so would be able to give the answer as 10. But, in this scenario (i.e. Powdermonkey being able to see nine villages) Firemonkey in seeing 4 villages would remain silent not being able to tell whether the answer is 10 or 13. Therefore, Powdermonkey could deduce that Firemonkey must indeed be seeing 4 villages and be able to answer 13 villages.

So clever Firemonkey would understand that Powdermonkey cannot see nine villages because, as we've seen, that would lead to an answer from one of them that presumably hasn't been forthcoming. Firemonkey can therefore deduce that Powdermonkey must only be able to see 6 villages, not 9. Firemonkey’s silence would not give away to Powdermonkey whether he can see 7 or just 4 villages and therefore Firemonkey can answer that there must be 10 villages (he sees 4 and Powdermonkey must be seeing 6). Does that make any sense? (I've rewritten this several times to try to clarify what I'm saying here, but I'm failing miserably I think)

[Sisyphus]

Good shot Marco, well done, you are on the right path.

They may or may not be seeing the same villages, the only thing they know is that between them they can see them all.

With firemonkey seeing 4 villages, powdermonkey could be seeing from 6 to 13.

Use your ideas but work from this position.

[Dougella]

Wow this is a real puzzler.

[Sisyphus]

It is fiendish but it is one of those where it can be solved in steps.

You can find bits of the answer but not be able to see how to use them until you have another bit. All of a sudden they all click into place.

I don't think I have given much away by saying this.

On the other hand we could start a revolution, rise up and overthrow the king, and release all the prisoners from the tower.

[Dougella]

^ Am I allowed to ask, if firemonkey can see the villages can he also see the people in them?

[Marco]

I think I've figured it out now that I'm charged up with two strong cups of coffee.

I reckon Firemonkey could solve in three days maximum if Powdermonkey is unable to give an answer, in which case the answer would have to be 10 villages.

Day ONE – Firemonkey (FM) knows that Powdermonkey (PM) can only possibly see 6 – 13 villages. Now if PM is unable to answer, FM can also deduce that PM is not seeing 11,12,13 villages. Likewise, PM would know that FM is not seeing 11,12,13 villages. Okay, so FM now knows that PM can only see 6 – 10 villages.

Day TWO – If FM isn’t forthcoming with an answer, PM would now know that FM isn’t seeing 0,1,2 villages because if he did, he would have deduced that since PM isn’t seeing 11,12 or 13 villages, there must be 10 villages.

Day THREE – If PM can see 8, 9 or 10 villages and now knows that FM isn’t seeing 0,1 or 2 villages, then he would call 13 villages. If PM stays silent, then FM must know he is only able to see 6 or 7 villages and therefore there can only be 10 villages!

[Sisyphus]

@ Dougella.

You can ask any questions you like.

Yes, I think he may be able to see the villagers.

It doesn't matter though, firemonkey is entirely confident that he will be released because he has full confidence in his cousin.

[Sisyphus]

@ Marco.

Well done.

That was quicker than I did it.

I think you have an off by one error on the day count though. They will not be sure that the other couldn't answer until the beginning of the next day. The timing is controlled by the jailer and may not ask until midnight. To be safe they must not call the result too early.

However the day count will not affect the answer so, yes, that was how he did it and there were 10 villages.

[Sisyphus]

No peeking at Marco's spoiler everyone.

[Marco]

Excellent! I'm quite pleased with myself lol. Do you want me to remove my answer, Sisyphus?

[Dougella]

Originally Posted by Sisyphus

@ Dougella.

You can ask any questions you like.

Yes, I think he may be able to see the villagers.

It doesn't matter though, firemonkey is entirely confident that he will be released because he has full confidence in his cousin.

Ah thank you. Well I guess help from the villagers is not included in getting the answer then, ok lol.

[Sisyphus]

What question would you ask anyway? How could you trust any answer?

The jailer probably comes from the village, would you trust them?

You now know that the puzzle can be solved with the information you already have because Marco did it.

I could give some spoilerd hints if you like or you could very quickly double click on the spoilers to get a feel of the answer without cheating too much.

[Dougella]

^ No I was thinking someone from the village could shout from one to the other or something, I was thinking too far outside the box lol.

[Sisyphus]

Hi Marco,

I think you can be double smug for that.

Let's be mean and leave the answers there to be a temptation.

It will be a sort of marshmallow test.

[Sisyphus]

^^ Thinking outside the box is good. Solving puzzles like this is good mental exercise.

You can learn as much from finding the wrong way to do it as you can the right.

Deep down I am a 'rescuer' and I want to help you solve the puzzle. That is why I have told you too much already.

[genovese]

So what you're saying is, you're gonna start a dedicated puzzle thread to keep us mentally stimulated and get us all through lockdown

Thank you, sir

[Sisyphus]

Sorry, no, I doubt I could keep it up.

Anyway, get back to the 10 Films thread, I have enough titles now to get me banned for a week.