Dividing Pizza with a Clock
Source: Alok Goyal Puzzle Page ( http://alokgoyal1971.com/ ) . Alok is ex-IIT Delhi, Partner at Helion VC Problem: Part I (Easy): Using a clock, divide a pizza among 12 people Part II (Difficult): Using a clock, divide a pizza among 11 people? Solution: Highlight the part between the * symbols for the answer. * Part I (12 people): cut along the radii pointing at the 12 hour marks - they are evenly spaced at 360/12 = 30 degrees, giving 12 equal slices. Part II (11 people): use the 11 moments in 12 hours when the hour and minute hands exactly overlap (12:00, ~1:05:27, ~2:10:54, ..., ~10:54:33). The minute hand gains 330 degrees per hour on the hour hand, so successive overlaps are 12/11 hours apart, and the overlap direction advances by exactly 360/11 degrees each time. Those 11 radii are therefore equally spaced - cutting along them divides the pizza into 11 equal slices. Bonus extension from the comments: minute and second hands overlap 59 times an hour - the ...