(12/5/95)

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MathMagic Cycle 19: Level 7-9 Regular 

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Counting your pennies

For this challenge you would need to fold a regular 8 1/2 by 11" piece
of paper in half. You need a lot of pennies and possibly a caliper.

What you will try to do is determine the maximum number of pennies that
you can place on top of that paper, if ONLY this two rules apply:

1) All pennies must be horizontal and have their centers INSIDE the paper

2) The center of any penny CANNOT be covered by another penny.
 
HINTS: The diameter of a penny is 3/4" and the centers of adjacent coins
can form equilateral triangles.

BONUS: How many regular hexagons are there? 

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MathMagic Cycle 19: Level 7-9 Advanced 

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The North Pole folks have to buy in bulk. While shopping for some hardware
items, one of the operators noticed that for identical crates of goodies,
two competing hardware stores had different prices. One was $1,122.00 and
the other was $2,210.00. Each crate was from the same manufacturer, and
had the same number of items. What are the possible costs for each item?

(HINT: Some may be under $1)

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Good luck and happy holidays
MrH