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You are a prisoner with two guards, each guarding one door to your cell. One guard always lies and one is always truthful, but you do not know which is which. You may leave your cell by one of the two doors. One leads to the execution block and death. The other to freedom. You may ask only one question, which you may address to either of the guards but not to both. What do you do? Difficulty rating: simple Buying cherries Cherries are very popular in South Africa. In one warehouse 1,000kg of fresh cherries are stored. The cherries contain 99% water when fresh, but a few days later, a test showed that there was now only 98% water, due to the drying out of the cherries. What do the cherries weigh now? Difficulty rating: basic Crazy dog John and Paul are on their bicycles, distance L apart. They begin at the same time to move towards each other, each pedaling as fast as they can intending to collide. At the instant they begin, their dog who loves them both leaves John and runs as fast as he can to Paul, who pats him on the head, at which point he turns and runs back to John. All this is repeated until the cyclists collide. How much distance is covered by the dog? Assume that John and Paul move with constant velocity v1 and v2, and the dog moves with speed u and is able to turn around instantly. Difficulty rating: challenging A bicycle problem
The year is 2007.Two days ago I was ten years old; Next year I shall be thirteen. What is the date today and when is my birthday? Difficulty rating: trivial Road map
Death circle N prisoners are to be put to death, except for one, who will be set free. The method to determine who will be set free is as follows: All prisoners stand in a circle. A gun is given to a prisoner 1, and he has to shoot dead the prisoner to his left. He then passes the gun to the next (alive) prisoner on his left, who, in turn will shoot the prisoner on his left, and pass the gun to the next person on his left, and so on. For example if N=5 prisoners are standing in a circle (call them prisoner 1, 2, 3, etc). - 1 shoots 2, and passes the gun to 3. - 3 shoots 4, and passes the gun to 5. - 5 shoots 1, and passes the gun to 3 (2 is already dead) - 3 shoots 5, and 3 is the last one left. He is set free. Who is set free for N=100. Any arbitrary N? Difficulty rating: hard Throwing dice In a pub the owner is throwing a number of dice simultaneously. "I am trying to get one of each of the six faces", he says, "But it hasn't happened yet". "No", I said "You need at least four more dice to make the odds in favour of such a thing" How many dice does the owner have? Difficulty rating: tricky Square field
Certain numbers can be expressed as a function of their own digits, while maintaining the order of the digits. For example 36=3! x 6. Can you find the formulation for 71, 119, 720, 733 and 936? (If you're feeling adventurous, try 24,739.) Difficulty rating: easy to hard Bottle of wine Three men order a bottle of wine at R30 to drink with their meal. They each pay R10 for it. The waitress asks the manager who only has a bottle at R25, so he gives the waitress the wine and R5 change. She returns to the table but gives only R3 back keeping R2 for herself. Since each man paid R10 and received R1 change he has paid R9. But 3 X 9 = R27 which with the R2 kept by the waitress makes R29. Where did the R1 go? Difficulty rating: really easy
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