Problems
Go, go, Power Arrangers! Everyone loves this team of five superhero high school students who wear the letters A, B, C, D, and E. When they stand side by side to confront evil monsters, they arrange their team in one of 120 possible different left-to-right orders, giving them various different tactical superpowers. They are even more popular than the Teenage Permutant Ninja Turtles!
Some critics of the show claim that the team only has its arrangment gimmick so that the owners of the show can sell 120 separate sets of 5 action figures, each of which features the team in a different left-to-right order, glued to a base so that the set cannot be rearranged. As an avid Power Arrangers fan, you have collected 119 of these sets, but you do not remember which set you are missing. Your 119 sets are lined up horizontally along a shelf, such that there are a total of 119 × 5 = 595 action figures in left-to-right order. You do not remember how the sets are arranged, but you know that the permutation of the sets is selected uniformly at random from all possible permutations, and independently for each case.
You do not want to waste any time figuring out which set you are missing, so you plan to look at the letters on at most F figures on the shelf. For instance, you might choose to look at the letter on the eighth figure from the left, which would be the third figure from the left in the second set from the left. When looking at a figure, you only get the letter from that one figure; the letters are hard to see, and the different team members look very similar otherwise!
After checking at most F figures, you must figure out which of the sets is missing, so you can complete your collection and be ready to face any possible evil threat!
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