In Conrad’s collection there are four royal gold five-pound coins. Conrad was told that some two of them were fake. Conrad wants to check (prove or disprove) that among the coins there are exactly two fake ones. Will he be able to do this with the help of two weighings on weighing scales without weights? (Counterfeit coins are the same in weight, real ones are also the same in weight, but false ones are lighter than real ones.)
Janine and Zahara each thought of a natural number and said them to Alex. Alex wrote the sum of the thought of numbers onto one sheet of paper, and on the other – their product, after which one of the sheets was hidden, and the other (on it was written the number of 2002) was shown to Janine and Zahara. Seeing this number, Janine said that she did not know what number Zahara had thought of. Hearing this, Zahara said that she did not know what number Janine had thought of. What was the number which Zahara had thought of?
The case of Brown, Jones and Smith is being considered. One of them committed a crime. During the investigation, each of them made two statements. Brown: “I did not do it. Jones did not do it. " Smith: “I did not do it. Brown did it. “Jones:" Brown did not do it. This was done by Smith. “Then it turned out that one of them had told the truth in both statements, another had lied both times, and the third had told the truth once, and he had lied once. Who committed the crime?
Elephants, rhinoceroses, giraffes. In all zoos where there are elephants and rhinoceroses, there are no giraffes. In all zoos where there are rhinoceroses and there are no giraffes, there are elephants. Finally, in all zoos where there are elephants and giraffes, there are also rhinoceroses. Could there be a zoo in which there are elephants, but there are no giraffes and no rhinoceroses?
Several natives of an island met up (each either a liar or a knight), and everyone said to everyone else: “You are all liars.” How many knights were there among them?