In the September 2014 issue of Math Horizons (page 8), Stan Wagon poses the following problem, which he says originated as a problem in the 1968 Moscow Mathematical Olympiad: A round cake has icing only on top. Cut out a piece in the usual shape (a sector of the circle), turn it upside down, and replace it to restore roundness. Repeat with the next piece; that is, move counterclockwise, cut out a piece with the same central angle, flip it, and replace it. Continue this process. If a piece has a knife cut from a previous iteration, ignore the cut and flip the piece as if it was solid. For pieces with 45 degree central angles, it takes 16 flips to return all icing to the top of the cake; if 180 degrees is used, it takes only four flips. How many flips does it take when the central angle is 181 degrees? Pete Winkler poses a similar problem in Mathematical Mind-Benders, which he says "was passed to me by French graduate student Thierry Mora, who heard it from his prep-school teacher Thomas Laorgue" (who didn't invent the problem and didn't know its origin). Does anyone have access to the 1968 Moscow Olympiad problems? If so, can he/she provide an English translation of the original problem? I'd be especially interested in knowing who is credited with inventing the problem (though often this kind of information is hard to dig up). Jim Propp