planetf1.com

The Three Gods

Three Gods A, B, and C are called, in no particular order, True, False, and Random. True always speaks truly, False always speaks falsely, but whether Random speaks truly or falsely is a completely random matter.

Your task is to determine the identities of A, B, and C by asking three yes-no questions; each question must be put to exactly one God. The Gods understand English, but will answer all questions in their own language, in which the words for yes and no are “da” and “ja”, in some order. You do not know which word means which.

It could be that some God gets asked more than one question (and hence that some God is not asked any question at all).
What the second question is, and to which God it is put, may depend on the answer to the first question. (And of course similarly for the third question.)
Whether Random speaks truly or not should be thought of as depending on the flip of a coin hidden in his brain: if the coin comes down heads, he speaks truly; if tails, falsely.
Random will answer “da” or “ja” when asked any yes-no question.
What would your three questions be?

Answer:

Q1: Ask god B, “If I asked you ‘Is A Random?’, would you say ja?”.
If B answers ja, either B is Random (and is answering randomly), or B is not Random and the answer indicates that A is indeed Random. Either way, C is not Random. If B answers da, either B is Random (and is answering randomly), or B is not Random and the answer indicates that A is not Random. Either way, you know the identity of a god who is not Random.

Q2: Go to the god who was identified as not being Random by the previous question (either A or C), and ask him: “If I asked you ‘Are you False?’, would you say ja?”.
Since he is not Random, an answer of da indicates that he is True and an answer of ja indicates that he is False.

Q3: Ask the same god the question: “If I asked you ‘Is B Random?’, would you say ja?”.
If the answer is ja, B is Random; if the answer is da, the god you have not yet spoken to is Random. The remaining god can be identified by elimination.


Does the answer make any sense to you? I'm totally lost. For example, how does the answer to the first question eliminate C from being Random when da and ja are not defined?

Would you ask different questions instead?

Here you go, I made this diagram to explain part 1:

http://imgur.com/oU59q2C.png

It's a case of compound binary logic, the Random mixes it up a bit, and the definition of the Random character's behaviour can alter the solutions a little, (ie, random can mean "it gives a random answer" or "it randomly decides whether or tell the truth" or "it's identity is randomly a truth teller or a liar for the duration of the puzzle" - but I think the solution you describe satisfies all cases.

The Random character is the big problem in this puzzle as you can't control their output. When you have a character who you know will always lie or always tell the truth you can control their behaviour even if you don't know which method they do. So the trick of the first question you ask is to be able to either identify random, or eliminate them. Because you may pick random, the only thing you can do is to identify a god who definitely isn't random.

If you pick Random, then it is certain that one of the others definitely isn't Random, however if you don't have Random, you need to ask a question that will allow you to know with certainty which of the other two isn't Random.

ie: if B *is* random it is a certainty that both A&C are not Random, so it doesn't matter that B answers randomly.

however: if B *isn't* random you need to have your answer enable you to identify who is Random, and then choose the other.

The Ja and Da is an extra layer of confusion, but it's basically building on basic logic principles of:

truth * truth = truth
false * truth = false
truth * false = false
false * false = truth

If you build tables like I did for the subsequent questions, you'll see how the puzzle works, but it's the first question that is the most important.

This makes me feel like my brain is made of mash potatoe.

for Alienturnedhuman.

I spent a while with a pen and paper and got some of it roughly worked out but I have to applaud your full in-depth explanation.

I do like a good brain frazzle in the morning

Just wish you hadn't put the answer in the OP. Reminds me of the riddle in The Labyrinth with the 2 doors, 2 creatures, 1 tells the truth and 1 lies and only 1 yes/no question to find out which door to gp through.

minchy wrote:I do like a good brain frazzle in the morning

Just wish you hadn't put the answer in the OP. Reminds me of the riddle in The Labyrinth with the 2 doors, 2 creatures, 1 tells the truth and 1 lies and only 1 yes/no question to find out which door to gp through.

If you were the other one would you tell me to go in there?

moby wrote:

minchy wrote:I do like a good brain frazzle in the morning

Just wish you hadn't put the answer in the OP. Reminds me of the riddle in The Labyrinth with the 2 doors, 2 creatures, 1 tells the truth and 1 lies and only 1 yes/no question to find out which door to gp through.

If you were the other one would you tell me to go in there?

Depends which door you're asking about.

minchy wrote:

moby wrote:

minchy wrote:I do like a good brain frazzle in the morning

Just wish you hadn't put the answer in the OP. Reminds me of the riddle in The Labyrinth with the 2 doors, 2 creatures, 1 tells the truth and 1 lies and only 1 yes/no question to find out which door to gp through.

If you were the other one would you tell me to go in there?

Depends which door you're asking about.

Either one, then go in the other if its yes

minchy wrote:I do like a good brain frazzle in the morning

Just wish you hadn't put the answer in the OP. Reminds me of the riddle in The Labyrinth with the 2 doors, 2 creatures, 1 tells the truth and 1 lies and only 1 yes/no question to find out which door to gp through.

I don't post as often as I used to, so I forgot how to hide it.

Alienturnedhuman wrote:Here you go, I made this diagram to explain part 1:

http://imgur.com/oU59q2C.png

It's a case of compound binary logic, the Random mixes it up a bit, and the definition of the Random character's behaviour can alter the solutions a little, (ie, random can mean "it gives a random answer" or "it randomly decides whether or tell the truth" or "it's identity is randomly a truth teller or a liar for the duration of the puzzle" - but I think the solution you describe satisfies all cases.

The Random character is the big problem in this puzzle as you can't control their output. When you have a character who you know will always lie or always tell the truth you can control their behaviour even if you don't know which method they do. So the trick of the first question you ask is to be able to either identify random, or eliminate them. Because you may pick random, the only thing you can do is to identify a god who definitely isn't random.

If you pick Random, then it is certain that one of the others definitely isn't Random, however if you don't have Random, you need to ask a question that will allow you to know with certainty which of the other two isn't Random.

ie: if B *is* random it is a certainty that both A&C are not Random, so it doesn't matter that B answers randomly.

however: if B *isn't* random you need to have your answer enable you to identify who is Random, and then choose the other.

The Ja and Da is an extra layer of confusion, but it's basically building on basic logic principles of:

truth * truth = truth
false * truth = false
truth * false = false
false * false = truth

If you build tables like I did for the subsequent questions, you'll see how the puzzle works, but it's the first question that is the most important.

That's brilliant.

Alienturnedhuman wrote:Here you go, I made this diagram to explain part 1:

http://imgur.com/oU59q2C.png

It's a case of compound binary logic, the Random mixes it up a bit, and the definition of the Random character's behaviour can alter the solutions a little, (ie, random can mean "it gives a random answer" or "it randomly decides whether or tell the truth" or "it's identity is randomly a truth teller or a liar for the duration of the puzzle" - but I think the solution you describe satisfies all cases.

The Random character is the big problem in this puzzle as you can't control their output. When you have a character who you know will always lie or always tell the truth you can control their behaviour even if you don't know which method they do. So the trick of the first question you ask is to be able to either identify random, or eliminate them. Because you may pick random, the only thing you can do is to identify a god who definitely isn't random.

If you pick Random, then it is certain that one of the others definitely isn't Random, however if you don't have Random, you need to ask a question that will allow you to know with certainty which of the other two isn't Random.

ie: if B *is* random it is a certainty that both A&C are not Random, so it doesn't matter that B answers randomly.

however: if B *isn't* random you need to have your answer enable you to identify who is Random, and then choose the other.

The Ja and Da is an extra layer of confusion, but it's basically building on basic logic principles of:

truth * truth = truth
false * truth = false
truth * false = false
false * false = truth

If you build tables like I did for the subsequent questions, you'll see how the puzzle works, but it's the first question that is the most important.

Hey, Alien, you were one of them kids who always put his hand up in maths cos you knew the answer, weren't you??

But then you do come from another world, so maybe you're Klaatu, just here on earth to test us inferior humans?

moose22 wrote:

Alienturnedhuman wrote:Here you go, I made this diagram to explain part 1:

http://imgur.com/oU59q2C.png

It's a case of compound binary logic, the Random mixes it up a bit, and the definition of the Random character's behaviour can alter the solutions a little, (ie, random can mean "it gives a random answer" or "it randomly decides whether or tell the truth" or "it's identity is randomly a truth teller or a liar for the duration of the puzzle" - but I think the solution you describe satisfies all cases.

The Random character is the big problem in this puzzle as you can't control their output. When you have a character who you know will always lie or always tell the truth you can control their behaviour even if you don't know which method they do. So the trick of the first question you ask is to be able to either identify random, or eliminate them. Because you may pick random, the only thing you can do is to identify a god who definitely isn't random.

If you pick Random, then it is certain that one of the others definitely isn't Random, however if you don't have Random, you need to ask a question that will allow you to know with certainty which of the other two isn't Random.

ie: if B *is* random it is a certainty that both A&C are not Random, so it doesn't matter that B answers randomly.

however: if B *isn't* random you need to have your answer enable you to identify who is Random, and then choose the other.

The Ja and Da is an extra layer of confusion, but it's basically building on basic logic principles of:

truth * truth = truth
false * truth = false
truth * false = false
false * false = truth

If you build tables like I did for the subsequent questions, you'll see how the puzzle works, but it's the first question that is the most important.

Hey, Alien, you were one of them kids who always put his hand up in maths cos you knew the answer, weren't you??

But then you do come from another world, so maybe you're Klaatu, just here on earth to test us inferior humans?

I want his brain.

Alienturnedhuman, you WERE on a TV show about speed dating weren't you!?

flyboy10 wrote:Alienturnedhuman, you WERE on a TV show about speed dating weren't you!?

Well it wasn't really about speed dating, it was about the science of dating websites and dating algorithms.

It's a couple of years now, but the story is quite entertaining with how it worked out:

I follow the mathematician who presented the show on Twitter, who I had seen a few lectures (on YouTube) where she spoke about the mathematics and game theory - and I had a few questions about flaws in her analogies, but was pointless raising them in the YouTube comments section... because it's the YouTube comments section.

Anyway, she posted on Twitter that she was doing a show about the science of dating and they needed volunteers to be matched so they could be used to demonstrate the different theories. I saw an opportunity to meet her and talk to her, so signed up, but because it was happening in London assumed I probably wouldn't be picked.

Anyway, 2 weeks before filming I get an email explaining that I have been selected, and their algorithm has found everyone a good match. So I turned up at the address - some nightclub in the middle of London - and there is a queue of people waiting, at the back of which is a group of young 18-21 year old girls all seemingly chatting. I quickly enquire if it's the correct line, and then patiently wait. Some people people turn up, ask me if it's the correct line,
I confirm, they look closer to my age so I ask them how they found out about the show. They say it was advertised on the BBC London website. I say "Oh,
I found it because I follow Hannah Fry on Twitter"

They say "Who's Hannah Fry" but the girl ahead of me in the queue (who it turned out was nothing to do with the 3 or 4 young girls all chatting) says "Oh I follow Hannah Fry, that's why I'm here"

Turns out she's a doctor of Mathematics from UK university (I'll call her M from now on), and she had seen the same tweet and thought it would be an interesting opportunity to meet her, as well as being a bit of fun. We end up chatting the different mathematical theories from her lectures on the game theory behind dating and wondering what they will test us on in the show.

They start letting people in to the night club, and we see they have to sign the standard NDA form, as well as getting a different coloured bracelet - we both conclude it's because they are dividing people into groups depending on how they matched. When we go up to be let in, we both get told "oh, you're on the list of people who were randomly selected to wear microphones" and we both get yellow bracelets.

We get wired up for mics, and then meets few other yellow wristbanded people. Everyone seems to be from a science/maths/tech background so we conclude maybe that's what we have in common, or analytical thinking. Sure enough, when the thing starts they tell us to go to a different part of the nightclub based on our wristband for speed dating. Before we start, Hannah Fry comes up and tells us "Hi guys, just to let you know, you guys are particularly well matched, so you should get on really well"

And sure enough, I get on really well with everyone I talk to.

After it finishes, we are asked to drop our bracelet into one of three baskets or or depending on how well we felt it went. I drop mine in

I then go to the bar, to get a drink, and some other women ask me how I got on in my group (they are from a different colour) - I say it went really well,
but they say theirs was really bad, but before they started, Hannah Fry had told them that their group was badly matched.

I then realise what's going on, find M and discuss - they've split us into four groups: Good match / Told was good , Good match / Told was bad , Bad match / Told was good , Bad match / Told was bad.

The reason was to determine what had the bigger influence: being told you were a good match, or actually being a good match on the algorithm.

I then spend the rest of the evening chatting with M, and then comes be the big reveal.

First - they confirm my theory about the four groups, and it turns out that the Good/Good were the happiest (all but 1 voted for ), Good/Bad and Bad/Good were roughly equal, and Bad/Bad the least satisfied.

They then reveal, that they paired everyone with a perfect match (it may not be their ultimate match, as some people were more than one other person's best match, but I'm assuming they probably used the stable marriage algorithm to get the best compatibility.

It turns out that my best match was M - the girl I met in the queue before the meeting even started and had spent 90% of my time chatting to since then. They also reveal we were by far and away the best matched couple at the event.

But it was not a surprise to either of it, because while neither of us had travelled down for the dating, that percularity alone meant it was likely we would be well matched (and we enjoyed talking to each other)

We had both travelled down primarily to meet Hannah Fry and secondly to watch the experiment from the inside.

It also explained why we had been "randomly" selected to wear mics, and why film crews had been glued to us the majority of the evening.

Anyway, I did get to chat to Hannah Fry, and when I said to her that you can't using optimal stopping theory on choosing marriage partners, she said "oh yeah, it's nonsense, I know, it's only put in as a bit of fun"

@Alien, that's so cool and thanks for the detailed explanation. I only watched that programme because of Hannah Fry and the ostensibly maths related content. If I were single, I'd probably have signed up to be on it (my thing is actually TV quiz shows).