is above . Most people's intuition is that it is in the thousands or tens of thousands, while others feel it should at least be in the hundreds. The correct answer is 23. The reason is that the correct comparison is to the number of partitions of the weights into left and right. There are different partitions for weights, and the left sum minus the right sum can be thought of as a new random quantity for each partition. The distribution of the sum of weights is approximately Gaussian, with a peak at and width , so that when is approximately equal to the transition occurs. 223 − 1 is about 4 million, while the width of the distribution is only 5 million. In fiction Arthur C. Clarke's novel A Fall of Moondust, published in 1961, contains a section where the main characters, trapped underground for an indefinite amount of time, are celebrating a birthday and find themselves discussing the validity of the birthday problem. As stated by a physicist passenger: "If you have a group of more than twenty-four people, the odds are better than even that two of them have the same birthday." Eventually, out of 22 present, it is revealed that two characters share the same birthday, May 23. Notes References Bibliography External links The Birthday Paradox accounting for leap year birthdays A humorous article explaining the paradox SOCR EduMaterials activities birthday experiment Understanding the Birthday Problem (Better Explained) Eurobirthdays 2012. A birthday problem. A practical football example of the birthday paradox. Computing the probabilities of the Birthday Problem at WolframAlpha Probability theory paradoxes Probability problems Applied probability Birthdays Mathematical problems Coincidence