Attempt to reconstruct the story: Professor O'Blivet blunders into a 7-11 and makes four purchases. He punches each price into his pocket calculator, but unwittingly uses the "*" (times) key instead of the "+" key to total them up. He is nevertheless amused to see the total 7.11, and is blissfully unsurprised when the clerk reaches the same total by adding properly. What were the four prices? Are half-cents still legal tender?-) 1.125, 1.28, 3.125, 1.58 Also, 1.185, 1.20, 1.60, 3.125 . rcs> Suppose we ignore the custom of rounding up (.645 -> .65), and allow (positive) rationals in the solution. It's not clear to me that the set of solutions is still finite, and my enumeration methods would only work if the denominators are bounded. E.g., .81, 5.00/3, 2.00, 7.90/3; .75, 1.96, 15.00/7, 15.80/7; .90, 10.00/7, 1.96, 19.75/7. ("Look, these are three for $5 and those are three for $7.90, and I *insist* on paying the exact price for one of each!") --rwg Spoiler: The intended answer: 1.20, 1.25, 1.50, 3.16