SINCERE AND LYING
One day, when I was travelling around India, the Napur guide told me: “There are two mythical animals showing you the path: the Kalik and the Kalek. In the columns with the sculpture of the Kalik, you always found two sentences: one is true and the other false; if the sculpture is a Kalek the two sentences are viceversa either both true or both false”.
The Golden Temple
Looking for the Golden Temple I arrived at an intersection between two roads: here was a column at the beginning of each road, but the animals on top of them were unrecognizable. On the right column I read: “At least one is a Kalek” and “Of the two, only one is a Kalik”, and on the left column: “The two animals are the same” and “To go to the Golden Temple take the left road”. Which road was leading to the Golden Temple?
The Black Temple
On the way to the Black Temple I arrived at an intersection between two roads with two columns (the animals on top of them were unrecognizable); on the column of the wide road I read: “At least one of the two is a Kalik” and “At least one of the sentences of the other column is true”, and on the column of the narrow road: “At least one of the sentences of the other column is true” and “This is the road that leads to the Black Temple”. Which road was leading to the BlackTemple?
SOLUTIONS
The Golden Temple
The road at the left was leading to the Golden Temple.
If there was a Kalik on the right column the two sentences would never be one true an the other false: that is, if on the left column there was another Kalik they would both be false, or if there was a Kalek they would be both true; so this means that on the right column there has to be a Kalek. So, the first sentence is true, and therefore also the second one, that is that the other animal (on the left column) is a Kalik. So, since the first sentence on the left column is false, the other one has to be true: to get to the Golden Temple one has to take the road on the left.
The Black Temple
The wide road was taking to the Black Temple.
If on the wide road column the animal was a Kalik, the first sentence would be true, and so the second one would be false: and this means that both sentences on the other column would be false; but since the first sentence of the first column is true, the animal of the wide road column has to be a Kalek. If on the first column both sentences were true, on the other column there would be a Kalik: the first sentence would be true and the second one false; but if on the first column both sentences were false, on the other one there would be a Kalek and the two sentences would both be false. In any case the sentence that says that the road to the Black Temple is the narrow one is false.