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## Usenet Newsgroups : rec.puzzles Hall of Fame

The rec.puzzles Hall of Fame is a compilation of over 500 of the most popular puzzles that have been posted and discussed in the rec.puzzles newsgroup. In most cases a detailed solution has been provided.

Many of these puzzles also appear in Braingle's own collection.

 rec.puzzles Newsgroup FAQ Hall of Fame alt.brain.teasers Newsgroup FAQ
Categories : pickover : pickover.15.p

```Title: Cliff Puzzle 15: Cherries in Wine Glasses
From: cliff@watson.ibm.com

If you respond to this puzzle, if possible please send me your name,
you provide unique information.  PLEASE ALSO directly mail me a copy of
your response in addition to any responding you do in the newsgroup.  I
will assume it is OK to describe your answer in any article or
publication I may write in the future, with attribution to you, unless
you state otherwise.  Thanks, Cliff Pickover

* * *

Consider a 9x9 grid of beautiful crystal wineglasses.  Throw 32 cherries
at the grid.  A glass is considered occupied if it contains at least one
cherry.  (With each throw a cherry goes into one of the glasses.)  How
many different patterns of occupied glasses can you make?  (A glass with
more than one cherry is considered the same as a glass with one cherry
in the pattern).

2.  Same as above except that you place 8 cherries in glasses (x,y) and
then determine the other positions by placing cherries at (x,-y),
(-x,y), (-x,-y) leading to 32 cherries in the grid.  Consider the array
of glasses centered at the origin.  How many different patterns of
occupied glasses can you make?  (A glass with more than one cherry is
considered the same as a glass with one cherry in the pattern).

3. Can your results be extrapolated to an NxN grid with M cherries
thrown at it for both problems?

```

Solution

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