2017/10/25 - Two Heads Are Better Than Three

[Buster]

By my math, my suggestion in the last post has a 50% chance of guessing correctly after the first pair of questions. After each pair of questions thereafter, there's a 33% chance of getting a guaranteed win, and a 50% chance of getting it right otherwise (overall 66% chance of getting it right per pair).

If anyone can get better odds than that, I'd be interested to hear it.

100% here

Ask the middle idol "if I ask the idol to the left if there's a mouse on my head, will it tell me the truth?" if the idol doesn't answer then the idol on the left is the random, if it answers then ask the idol on the right about the idol in the middle, if it doesn't answer then the middle is random, if it answers then the one on the right is the random
An idol can't answer if you ask them about the random idol because it doesn't know if it will tell truth or lie
An idol can answer if it answers randomly or the idol to the left of that idol tells the truth or a lie
something like this:
idols= Truth Liar Random answer=X
TLR
-XX
LTR
-XX
TRL
-X?
LRT
-X?
RTL
-?X
RLT
-?X

That solution only works if the objective is to identify the random head. If you need to identify all three, or get some key piece of info from them it falls short.

[Sleet]

The solution: That isn't actually the way forward. Go somewhere else.

[Istaran]

By my math, my suggestion in the last post has a 50% chance of guessing correctly after the first pair of questions. After each pair of questions thereafter, there's a 33% chance of getting a guaranteed win, and a 50% chance of getting it right otherwise (overall 66% chance of getting it right per pair).

If anyone can get better odds than that, I'd be interested to hear it.

100% here

Ask the middle idol "if I ask the idol to the left if there's a mouse on my head, will it tell me the truth?" if the idol doesn't answer then the idol on the left is the random, if it answers then ask the idol on the right about the idol in the middle, if it doesn't answer then the middle is random, if it answers then the one on the right is the random
An idol can't answer if you ask them about the random idol because it doesn't know if it will tell truth or lie
An idol can answer if it answers randomly or the idol to the left of that idol tells the truth or a lie
something like this:
idols= Truth Liar Random answer=X
TLR
-XX
LTR
-XX
TRL
-X?
LRT
-X?
RTL
-?X
RLT
-?X

That's nice, if it works that way. It depends on some assumptions though.

For one, you assume they can't answer if they lack knowledge of the correct answer, and that they also lack magical precognition or other means of determining what the random head would answer. If they can determine what the random head would answer, then they would give an effectively random answer to your question when the random head is to the left.

Accepting that assumption, you further assume that 'I can't confidently answer that question' is expressed as silence. There are some other possibilities. One is that in their language 'bo' means 'definitely yes', and 'lal' means 'not definitely yes'. (But we don't know this up front.) If this is the case, any combination of answers you get could map to any of the three being the random one. And you don't actually sort out which answer is yes or no in the process, so the second round is no better off than the first. By my math, after determining yes/no, you'd get up to 7/12 chance, or 57% per pair of questions.

If your assumptions hold, though, then great!

That solution only works if the objective is to identify the random head. If you need to identify all three, or get some key piece of info from them it falls short.

We are told in the comic the objective is to identify the random head, so we're good there at least.

[CHAOKOCartoons]

The solution: That isn't actually the way forward. Go somewhere else.

This is just how you find one of the collectables, the main path is actually a literal cakewalk.

[Buster]

oops missed that line.

Wait, Easy solution.

ask the same question twice, or two questions that have the same answer. keep trying until the one you're talking to changes his answer on the second question.

[Naro Rivers]

The problem is you can’t understand what each idol is saying. And I think they’re required to answer with something.

Part of the rules is that one head always answers truthfully, one always answers falsely, and one always answers randomly. If the true head can't answer truthfully,
it can't answer at all. The same is true of the false head. Only the random head will be able to answer everything.

That's nice, if it works that way. It depends on some assumptions though.

For one, you assume they can't answer if they lack knowledge of the correct answer, and that they also lack magical precognition or other means of determining what the random head would answer. If they can determine what the random head would answer, then they would give an effectively random answer to your question when the random head is to the left.

Accepting that assumption, you further assume that 'I can't confidently answer that question' is expressed as silence. There are some other possibilities. One is that in their language 'bo' means 'definitely yes', and 'lal' means 'not definitely yes'. (But we don't know this up front.) If this is the case, any combination of answers you get could map to any of the three being the random one. And you don't actually sort out which answer is yes or no in the process, so the second round is no better off than the first. By my math, after determining yes/no, you'd get up to 7/12 chance, or 57% per pair of questions.

If your assumptions hold, though, then great!

In every other instance of this riddle (at least as far as I've seen), even if some details are different, these assumptions are true. The true and false entities do not know how the random entity will answer, being unable to answer is expressed as silence, and the words mean "yes" and "no".

[Argent]

Part of the rules is that one head always answers truthfully, one always answers falsely, and one always answers randomly. If the true head can't answer truthfully,
it can't answer at all.

And, apparently, explodes.

[NHWestoN]

Looking at her facial expression, the next head to explode just may be Tarot's.....