TOT 191 1988 Autumn J4 2identical cogwheels with 14 teeth each
Source:
March 6, 2021
number theorycombinatorics
Problem Statement
(a) Two identical cogwheels with teeth each are given . One is laid horizontally on top of the other in such a way that their teeth coincide (thus the projections of the teeth on the horizontal plane are identical ) . Four pairs of coinciding teeth are cut off. Is it always possible to rotate the two cogwheels with respect to each other so that their common projection looks like that of an entire cogwheel?
(The cogwheels may be rotated about their common axis, but not turned over.)(b) Answer the same question , but with two -tooth cogwheels and four pairs of cut-off teeth.