MathDB

246

Part of 1953 Moscow Mathematical Olympiad

Problems(1)

MMO 246 Moscow MO 1953 11 gears on a plane

Source:

8/9/2019
a) On a plane, 1111 gears are arranged so that the teeth of the first gear mesh with the teeth of the second gear, the teeth of the second gear with those of the third gear, etc., and the teeth of the last gear mesh with those of the first gear. Can the gears rotate?
b) On a plane, nn gears are arranged so that the teeth of the first gear mesh with the teeth of the second gear, the teeth of the second gear with those of the third gear, etc., and the teeth of the last gear mesh with those of the first gear. Can the gears rotate?
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