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IMSO 2019 - Math Division - Exploration Question 3

IMSO Maths · IMSO 2019 - Math Division - Exploration

Question 3

Given the diagram below. Find as many ways as possible to put 7 more gears into the triangular board so that we can move the gears B and C simultaneously by moving the gear A. (Gears can be mounted only on the given points and a gear can move another gear only if the two gears are mounted around adjacent dots.)

Question illustration

For example, we can put 7 more gray gears as in the following picture to be able to move the gears B and C simultaneously by moving the gear A.

Question illustration