The muffin problem is fascinatingly both simple to ask and hard to solve. In spirit it reminds me of the Egyptian Fraction Problem, to not only represent the arbitrary p/q > 0 as a sum of distinct integer reciprocals (i.e., an Egyptian fraction), but to do so such that the largest denominator used is minimum. ((( It's well known that the greedy algorithm is not the way to solve this. E.g. -- as found in Wikipedia -- greedily: 5/121 = 1/25 + 1/757 + 1/763309 + 1/873960180913 + 1/1527612795642093418846225, but altruistically: 5/121 = 1/33 + 1/121 + 1/363. ))) QUESTION: Is there an algorithm for solving this minimization problem? As with the muffin problem there is also the question here of which decomposition uses the fewest summands. --Dan _____________________________________________________________________ "It don't mean a thing if it ain't got that certain je ne sais quoi." --Peter Schickele