# Fun with Fundamentals: Problem 164

Aug. 1, 2000
Paper workout and Solution to Problem 163. Quality control is only as good as the paper it’s written on, as this month’s problem by Richard A. Wyatt of Beloit, Wis., demonstrates

Paper workout

Problem 163 — Quality control is only as good as the paper it’s written on, as this month’s problem by Richard A. Wyatt of Beloit, Wis., demonstrates.

A crowd of people in well-cut business suits were gathered in the incinerator room of the Lee Key Hydraulic Co. The company had passed the test for ISO 9000 certification, and all that remained was to get the documentation copied.

As president Horatio Puff paced back and forth, mentally rehearsing his acceptance speech, newly appointed vice president of quality, Lucius Bluff struggled with the 50-lb box of audit documents. With a greatly audible sigh, Bluff heaved the box onto the horizontal conveyor leading to the incinerator and mopped his forehead.

At this same time Puff, bowing to imaginary applause, accidentally started up the conveyor. Everyone watched in horror as the box sped towards the conveyor at an instantaneous rate of 25 mph. Bluff shrieked and pushed the emergency brake as Puff raced towards the incinerator, hoping to push the box off the conveyor before it went in. The conveyor came to an instantaneous stop just as the box was 65 ft from the incinerator, and the box began to slide to its doom. Puff reached the incinerator in 2 sec (from the time the brake was thrown).

If the coefficient of friction between the box and conveyor belt is 0.30, and the box does not tip over, will Bluff’s dreams of TQM go up in smoke?

Fun with Fundamentals
POWER TRANSMISSION DESIGN
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Cleveland, OH 44114-2543

Solution to last month’s problem 163 — You know a perfect square when you see one, if you answered 10. Here’s how Chief Adi Omen can afford to be magnanimous for nine more birthdays:

The number of times any cell would be visited is equal to the number of divisors in the cell number. For instance, Cell 35 would be visited in the first round, the fifth round, the seventh, and the thirtyfifth, since its divisors are 1, 5, 7, and 35. Starting with a closed cell, it will be alternately opened, closed, opened, and finally closed.

Almost all numbers have an even number of divisors, since they come in pairs, i.e.1 x 35, 5 x 7. The exception are the perfect squares, and between 1 and 100 there are ten of them: 12, 22, 32, 42, 52, 62, 72, 82, 92 and 102. These numbers have an odd number of divisors,since one number is repeated, and so the prisoners in Cells 1, 4, 9, 16, 25, 36, 49, 64, 81 and 100 will go free.

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