==> 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, address, affiliation, e-mail address, so I can properly credit you if 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?