# Want To Visit MIT?

The picture above shows a part of a mechanical contraption exhibited in the main gallery of the MIT museum. The contraption begins with a motor (on the left) turning at $$212\ \textrm{rpm}$$. It is connected to a sequence of $$N$$ worm-gears, which can be seen in the picture. Each worm-gear pair reduces the rotation speed by a factor of $$f=50$$. The axle of the last gear in the sequence is embedded in a concrete wall that cannot rotate at all.

Find the smallest $$N$$ that will suffice to keep the exhibit running for a century.

Details

• Each wheel has approximately 50 teeth.
• The system jams when the final wheel needs to rotate by half a tooth.
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