Liesl+H.

media type="custom" key="10606658" I don't know if this helps at all but it seems similar to the Sasha and Avery problem
 * ** Meeting Probabilities ** ||
 * Given n independent random variables, each evenly distributed over the interval 0 to 1, the probability that all n are within q of each other (for any q < 1) is ||
 * [[image:http://mathpages.com/home/kmath124/kmath124_files/image001.gif width="461" height="25"]]  ||
 * This can be derived in several different ways. For example, we can divide the unit interval into k equal segments, and note that the probability of n randomly selected points all falling within j consecutive segments corresponds approximately to the probability that all n points fall within q = (j/k) of each other. This correspondence becomes exact in the limit as k goes to infinity (holding q constant). Equation (1) can also be derived from a geometrical point of view. Given a unit "cube" in n dimensions, equation (1) represents the fraction of the cube's content ("volume") consisting of points with orthogonal coordinates [x1, x2, ..., xn] such that |xi - xj| < q for all i,j. (See [|The Shape of Coincidence] for more on the geometrical aspects of this equation, and its relation to the rhombic dodecahedron.) ||
 * One possible generalization of this is to allow different tolerances on the different events. For example, suppose each of n people are to arrive at a certain location at some randomly chosen time between 1:00 PM and 2:00 PM, and each person will wait a certain amount of time before leaving. Say, for example, with n = 2 people, one can wait for w1 and the other can wait for w2 (both expressed as fractions of the total time interval). What is the probability that they will meet? Geometrically it's easy to see that this is just given by the are of the shaded region in the unit square shown below: ||
 * [[image:http://mathpages.com/home/kmath124/kmath124_files/image002.gif width="276" height="267"]]  ||
 * The shaded area equals to total square area minus the two excluded triangles, so we have ||
 * [[image:http://mathpages.com/home/kmath124/kmath124_files/image003.gif width="427" height="51"]]  ||
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 * [[image:http://mathpages.com/home/kmath124/kmath124_files/image002.gif width="276" height="267"]]  ||
 * The shaded area equals to total square area minus the two excluded triangles, so we have ||
 * [[image:http://mathpages.com/home/kmath124/kmath124_files/image003.gif width="427" height="51"]]  ||
 * [] ||
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