# The blind one who sees all

A blind prisoner is offered a deal by a king. 3 monks will be sent to his cell over a period of three days,only one monk will be sent to the prisoner's cell on any day. The king may decide to send one monk thrice or all monks might get to visit the prison once or any other combination. 2 out of the three monks always lie, they lie in such a way that whatever they say, there is no possible way for the truth to be interpreted by the listener . The remaining monk always conveys the exact Truth. The prisoner is allowed to ask only one question to each monk per day and the monks are strictly ordered to answer only with a "yes" or a "no" orĀ and if there is no way for the liars to lie and the truth speaker to convey the exact truth by speaking, they leave the room and the prisoner knows about this mannerism of theirs.

At the end of three days, the prisoner is presented before the king and if he is able to point out the nature of the monk who visited him each day and the exact day on which the monk visited him. If he is successful he is set free and if he is not he is sentenced to death. A liar meets him on the first day.

Suggest a possible way in which the prisoner can guarantee his freedom.

Notes: 1)The prisoner does not need to exactly identify the monk who visited him on a particular day. He is blind and it is impossible.

2)For instance, if one liar met the prisoner on the first and second day and the second liar met him on the third,the prisoner's answer to the king should be "a liar met me on the first day, he met me again on the second day and a different liar met me on the third". In this case he will be set free as he has pointed the exact nature (truth speaker/liar)of the monks who have met him and also the exact days on which the monks have met him.

• The first two paragraphs describe a good puzzle, however, the notes makes it confusing. So does the blind man need to identify whether the monk on each day is a liar or not, or does he need to know which ones are the same monk? What does "A liar meets him on the first day" mean? Does the blind man knows this? – justhalf Nov 19 '20 at 8:15
• Yes the blind man needs to identify whether a monk is a liar or not. "A liar meets him on the first day" means a liar or a lying monk meets him on the first day nothing extra to be deduced from that apart from the nature of the monk on the first day. The blind man does not know this. – Roshan Kandukuri Nov 19 '20 at 8:40

## This is not a solution, but rather an addition and explanation for the original solution

I am digging into some philosophy here, but I am in a mood to challenge Roshan's views on this problem, and I believe my view can make the solution much more acceptable in terms of logic.

Statement: There is no physically possible question to which truthful monk will ever give an answer.

By the puzzle's logic, answer "no" to the question "Did you answer 'no' to my question yesterday?" does not give the exact truth, since it does not give you a proper information on what happened yesterday. However, there are still too many variables in life, that are not covered by this question. For example, the full order of monks coming, the private life of the king, or the monastery, and et cetera. The only way to make the truthful monk speak is to state all the variables of the universe in a single sentence (or deny all of them, to make the monk say 'no') which is not really possible in these conditions.

That makes me extend your suggested solution, namely:

Truthful monk will not answer to the question "Am I alive?", since his answer "yes" will not be the exact truth - there are certain aspects of blind man's life, not covered by this "yes", namely heartrate, age, weight, and even expected longevity.

That makes your solution work without the assumption, that the liar comes in on the first day - you can just keep asking the same question every day as long as you hear the silence.

I must prevent the question about the other part of the solution - it is reasonable. Let's look into it case by case:

1. Asking "Were you the liar, that answered 'no' on a particular day?" to that certain liar. Though the answer "Yes" is not the exact truth, it can be understood as the exact truth, since it gives two facts, that are both true - and they can be extended by all the facts to the "exact truth". Thus, the liar can't answer this. He can answer "no", never the less - it would mean that one of this facts is false, making the blind man unable to understand it as truth.

2. I wanted to do the same for the second liar, but it is actually self-evident and you can do it yourself.

P.S: I'll rate the puzzle up, however, if you have a different understanding of "exact truth", please comment on it, so I could rate it down if I find it not satisfactory :D

• Firstly, great work thomas, even though you've gone far overboard to the what exact truth in this case means,I'm really happy that someone finally understood the essence of the puzzle.Here, exact truth is unique, singular and most importantly unambiguous (having only one interpretation). An exact lie is where all possible interpretations of the statement are not true.This question is representative of the behaviour of a complete truth teller and a complete liar. – Roshan Kandukuri Nov 19 '20 at 14:28
• Why does "exact truth" need to include every single fact about the universe for the truth-teller, but only need to be 'extendible' for the liar? This seems very inconsistent. – Deusovi Nov 19 '20 at 14:32
• Because for a given configuration of facts in the universe or freezing the universe at a point of time, a truth can be generated. Even a minor omission or mistake in a statement can make it a lie, I know this is far fetched from normal everyday truth and lie but rigid and acceptable nonetheless, for it is a modification in assigning truth values to a statement. – Roshan Kandukuri Nov 19 '20 at 14:48
• For example, Roshan is a boy is true and any other statement made on my gender implying anything else other Than the fact that I am a boy is false. – Roshan Kandukuri Nov 19 '20 at 14:49
• I've just defined absolute truth. The definition already exists, I've just incorporated it into a puzzle – Roshan Kandukuri Nov 19 '20 at 14:52

We know that a liar meets the monk on the first day. The questions should be targeted primarily towards finding out nature of the monk. It is crucial that the prisoner deduces the nature of the monk who met him on the first day.

A possible strategy to escape death: Day 1 "Am I alive?" Since we know that a liar was sent in first, he will answer with a 'no'. This is enough information for the prisoner to deduce that the monk lies.

Day 2 "Did you answer 'no' to my question yesterday?" This question is really crucial and a lot of information can be deduced from the answer provided. Now, let us examine the following 3 cases:

Case 1 Truth speaking monk.

If the monk who visited him on the second day was the truth speaker,he would leave the room.

He can't say yes because he would be lying. He can't say no because if he said no, then he won't be speaking the exact truth. Let me elaborate,now, we know that if he says no,the prisoner can interpret it in 2 different ways, those being : 1)he didn't answer any question yesterday.

2)he answered 'no' to the question yesterday.

We know that the monk who speaks the truth only speaks the exact truth and nothing else. If he was to say no, he would be leaving the prisoner with 2 possible interpretations. Hence, since there is no possibile way for him to convey the exact truth, he leaves the room.

Case 2 Same monk from day 1 In this case, the monk would lie by saying 'no'.

Case 3 The second liar In this case the monk says yes. The monk didn't meet the prisoner on day 1,initially it might seem like it is possible for him to say 'no'Ā  because he would be lying then too. Upon closer examination, it can be deduced that he won't be saying no because that answer can have 2 interpretations, and from our knowledge regarding the monks who lie, they lie in such a way that there is no possibile way for the listener to interpret the truth, and If this monk were to say no, the prisoner could interpret one of the 2 interpretations which is the truth. The liar thus is forced to lie by saying yes.

Day 3 "did you answer 'no' to my question 2 days ago?". The Same deductions for each of the three possibilities.

Since the prisoner is perfectly logical, he is able to deduce the required information to set himself free.

• Why are you answering your own question so early on? – Prince Deepthinker Nov 19 '20 at 8:45
• It's there for reference, its your choice to whether to view it or not. I realised that my question may seem too general to someone who wants to or has an inclination towards solving short puzzles, so I felt I should just post it there to make sure that a person who just skips down to the comment section to express his disdain finds out that this puzzle is not too general, after all. – Roshan Kandukuri Nov 19 '20 at 8:48
• Your answer contradicts the question's premise. Especially this one: "they lie in such a way that whatever they say, there is no possible way for the truth to be interpreted by the listener". – justhalf Nov 19 '20 at 8:49
• Just half no it doesn't, read between the lines. – Roshan Kandukuri Nov 19 '20 at 8:50
• In your answer, the prisoner is able to know that the monk lies, then it is not true that "there is no possible way for the truth to be interpreted by the listener". Maybe the question needs to be rephrased if that's not what you mean. – justhalf Nov 19 '20 at 8:51