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Motion System Design
Fun With Fundamentals: Problem 202

Fun With Fundamentals: Problem 202

Border incident
Problem 202
— A stitch in time can save more than nine, as this month’s problem by Leon G. Wilde of Andover, Mass., demonstrates.

Grandma was sitting in her rocker sewing, when her grandson Horton, just graduated from college, burst in the door.

“What are you sewing, grandma?” asked Horton.

“A new pillow cover,” replied Grandma. “I’m doing cross stitch. It’ll have 35,953 stitches all neatly arranged in rows and columns when it’s done. There are 10 stitches to the inch.” “How wide is the border,” asked Horton in awe.

“The border is the same width all the way around. There will be 22,113 stitches inside the border. You just got your Ph.D in mathematics,” exclaimed Grandma. “Figure it out yourself!”

Horton went up to his room and was a picture of fierce concentration. After two hours he was still stumped.

“I’m getting nowhere, grandma,” he stated. “I need more information.”

“Nonsense, boy,” exclaimed Grandma. “I’ve already told you all you need to know. But if you insist, I’ll give you a little hint.

“The length of the one I’m doing now is exactly the same as the width of the last one I did. That one had 15,229 cross stitches.” There are no half or quarter stitches. All stitches are full 1/10 in. stitches.

How wide is the border?

Send your answer to:

Fun With Fundamentals
1100 Superior Ave.
Cleveland, OH 44114-2543

Deadline is March 10. Good luck!

Technical consultant, Jack Couillard, Menasha, Wis.

Solution to last month’s problem 201 — You’re 100% correct, if you answered 52 days. Here’s the rate of decay for Mrs. Von Schlump’s backyard fetes.

We know that the pond is completely covered with algae every 81 days after cleaning, and we also know that the number of individual alga cells doubles every three days. We can construct the following table using percentage of pond covered (A) and corresponding percentage of visibility (100% 2A). The trick is to work backwards.

Mrs. Von Schlump’s restaurant bill was the talk of the town!

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