Let's refer to the classic prisoners and boxes puzzle I proposed previously on puzzletweeter. I am restating the problem here for convenience: This is the classic prisoners and boxes puzzle: There are 100 prisoners numbered 1,2,... 100 and 100 boxes. Each box is numbered and the number is stored inside the box as a label. The boxes are identical, there's no way to tell … Continue reading the story "prisoners and boxes - converse"
Monthly Archives for April, 2013
An integer point in a plane is a point whose coordinates are integers. Suppose we arbitrarily choose 5 integer points in a plane. Show that we can always find 2 among these 5 integer points such that the line segment joining the 2 points contains at least 1 more integer point. via MAA
We all feel like politicians are 4-legged animals. Well, can you argue that more than 99% of the politicians have more legs than average? via Prof. Berlekamp in the 2013 Kailath lecture Hint: ... ... ... ... ... ... ... ... ... ... ... ... One of the politicians broke one of his legs in the Vietnam war.
A man is sitting in a pub feeling rather poor. He sees the man next to him pull a wad of £50 notes out of his wallet. He turns to the rich man and says to him, "I have an amazing talent; I know almost every song that has ever existed." The rich man laughs. The poor man says, "I am willing to bet you all … Continue reading the story "What song?"
You are a prisoner sentenced to death. The Emperor offers you a chance to live by playing a simple game. He gives you 50 black marbles, 50 white marbles and 2 empty bowls. He then says, "Divide these 100 marbles into these 2 bowls. You can divide them any way you like as long as you use all the marbles. Then I will blindfold you … Continue reading the story "Life or death"
Let a be irrational. Show that there exist infinitely many rational numbers r = p/q such that . via cut the knot
You are given 6 cubes (A, B, C, D, E and F). You know that one of the cubes A, B and C weighs 2Kg, the other 4Kg and the third 6Kg, but you do NOT know which of them weighs 2Kg, 4Kg or 6Kg. You also know that the possible weights of the cubes D, E and F are 1Kg, 3Kg, and 5Kg. Again you do not know … Continue reading the story "Weighing"
Suppose there is a parking area which has parking lot for 24 cars. Each car is given its own parking lot . Suppose , on a particular day , 1st car has parked wrongly in some other parking lot . Remaining cars will park the car in its own lot if its available otherwise they will also park wrongly . Whatis the probability that the … Continue reading the story "Parking lot probability"