(12/5/95)

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MathMagic Cycle 19: Level 4-6 Regular 

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Concert Stash

The North Pole elves were hoping Mr.and Mrs.Claus would relax as much as
possible before the Christmas Season, so they convinced them to go to a 
concert that cost $25 each. It was their treat. The Elves all had col-
lected a few $10, $5,$1, half dollars and quarters from their own stashes, 
but first had to figure out in how many different ways they could come up with 
the money for the concert, since each one wanted to give some of
their money. It took them a while, but I bet MathMagicians could come up
with all choices really fast... Well, can you?

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MathMagic Cycle 19: Level 4-6 Advanced 

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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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Good luck and happy holidays
MrH