Find a 9-digit number, which you will gradually round off starting with units, then tenth, hundred etc., until you get to the last numeral, which you do not round off. The rounding alternates (up, down, up ...). After rounding off 8 times, the final number is 500000000. The original number is commensurable by 6 and 7, all the numbers from 1 to 9 are used, and after rounding four times the sum of the not-rounded numerals equals 24.
A beggar on the street can make one cigarette out of every 6 cigarette butts he finds. After one whole day of searching and checking public ashtrays the beggar finds a total of 72 cigarette butts. How many cigarettes can he make and smoke from the butts he found?
A man started to town with a fox, a goose, and a sack of corn. He came to a stream which he had to cross in a tiny boat. He could only take one across at a time. He could not leave the fox alone with the goose or the goose alone with the corn. How did he get them all safely over the stream?
James Bond is caught up in a mysterious scenario where the evil villain has him blindfolded. He somehow breaks through the handcuffs but is unable to get the blindfold off. Upon searching, he comes across a bow and 3 arrows. He can hear the villain speak, and thus tries to take a shot at him. He launches the first arrow, it misses the villain. He then launches the second arrow and it misses by a greater margin.
What is the probability that this third shot our James bond takes will be worse than the second shot?
Four people need to cross a rickety bridge at night. Unfortunately, they have only one torch and the bridge is too dangerous to cross without one. The bridge is only strong enough to support two people at a time. Not all people take the same time to cross the bridge. Times for each person: 1 min, 2 mins, 7 mins and 10 mins. What is the shortest time needed for all four of them to cross the bridge?
You are a cab driver who pools passengers. You pick 3 people from a destination and drop 1 after an hour. 2 people climb aboard at the same time and you drop 3 at the next destination. After some time, you pick 2 passengers only to drop 1 after a short distance where 3 more passengers climb up the cab. You leave the rest of the passengers one by one to their destination and then come back home.
