Two players in turn paint the sides of an \(n\)-gon. The first one can paint the side that borders either zero or two colored sides, the second – the side that borders one painted side. The player who can not make a move loses. At what \(n\) can the second player win, no matter how the first player plays?
So, the mother exclaimed - “It’s a miracle!", and immediately the mum, dad and the children went to the pet store. “But there are more than fifty bullfinches here, how will we decide?,” the younger brother nearly cried when he saw bullfinches. “Don’t worry,” said the eldest, “there are less than fifty of them”. “The main thing,” said the mother, “is that there is at least one!". “Yes, it’s funny,” Dad summed up, “of your three phrases, only one corresponds to reality.” Can you say how many bullfinches there was in the store, knowing that they bought the child a bullfinch?
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?
In a 10-storey house, 1 person lives on the first floor, 2 on the second floor, 3 on the third, 4 on the fourth, ..., 10 on the tenth. On which floor does the elevator stop most often?