THE’riddle of the gods three hermits it is a puzzle that allows us to think about logical paradoxes. The situation is this: we are lost in the mountains, without a cell phone or a map and we would like someone to help us get home. Luckily, an isolated house appears in front of us. It seems inhabited and we decide to go and ask for directions. When we get closer, we see that outside the door there is a sign that says:
Three hermits live here: one always tells the truth (he is sincere), one always lies (is liar), and one sometimes lies and sometimes tells the truth (it is random).
As soon as we enter, the three hermits come forward. The first tells us: “I am not sincere.” The second: “I’m not random.” The third: “I’m not a liar.”
We would like to be able to ask “sincere”, the only person who always tells the truth, for directions back home. But how do we find out who is “random”, who is “sincere” and who is “liar”? Let’s see it together.
The solution to the riddle of the three hermits
To understand who is the only person who always tells the truth, let’s analyze the statements one at a time. There first person told us to don’t be honest. So:
- If she were sincere, the sentence “I am not sincere” should be true, because sincere people always tell the truth. This, however, would create a paradox: she is sincere, but she is telling us that she is not. So it’s not sincere.
- If she were a liar, then she would have told us a lie, because liars always lie. So the sentence “I am not sincere” should be false, but since this person is actually not sincere, it would also be true, creating a paradox. So she’s not a liar.
Consequently, the first person must be “random”. In this case he actually told us the truth: it is not sincere, because it is random. The other two, therefore, will have to be “sincere” and “liar”.
There second person told us to don’t be random. We know this statement is true, because we have already found the random person. Consequently, the second person must be the one who tells us the truth, i.e “sincere”.
At this point we only have the third person left, who told us to Don’t be a liar. By exclusion, the third person must be a “liar”. So let’s check that everything comes back. If the third hermit were a liar, he could only tell us lies and the sentence “I am not a liar” would have to be false. Indeed, his statement is false and our third person is indeed a “liar”.
At this point, we are sure that we have not made any mistakes and we can ask the second hermit the way back, certain that he will show us the right path.
The riddles of the “knights and knaves”
This type of riddles takes inspiration from famous people logical problems called “of knights and knaves”, in which some characters always tell the truth (i knights) and others always lie (i scoundrels). The best known is “the riddle of the two doors”, which also appeared in the film Labyrinth. The term “knights and knaves” was coined by Raymond Smullyan, logician and puzzle creator, also author of the “troll’s riddle” and the “world’s most difficult puzzle”.
In the classic version, the puzzles are set on imaginary islands inhabited by knights and knaves, and involve a visitor to the island whose goal is to figure out who is a knave and who is a knight or uncover hidden information, all while being able to ask very few yes/no questions.
These puzzles may seem like just a game, but they train fundamental skills: deduction, management of ambiguity, reasoning by contradiction. Precisely for this reason, they are often used at school for train logical-mathematical thinkinglearn to think rigorously and to introduce some basic concepts ofboolean algebra, that branch of mathematics in which variables can take on only two values: “true” (1) or “false” (0). Boolean algebra is fundamental in the design of electronic circuitsin the logic of programming languages and also in more theoretical fields such as the study of chance. Approaching these topics through puzzles allows you to build solid intuitions before tackling mathematical abstraction.
