Source: Pertsel Vladimir, c/o internet newsgroup rec.puzzles. Used as Ken's POTD 6/1/94.
All solvers showed that there are solutions for any even number of coins (>=16). There are no solutions for an odd number of coins: Let n be the # of coins. Then each coin touches 3 others, so there are 3n/2 touches, since each touch is counted twice. Hence n must be even.
In general, arrange 4 coins into the shape of a diamond, with coins 2 and 3 touching each other and coins 1 and 4 touching 2 and 3 from opposite sides. Several of these diamonds can be arranged in a circle to satisfy any multiple of 4 coins greater than 16. Any group of 4 can be easily be replaced by a group of 6, by putting two coins between 2-3 and 4. For 24 coins, the configuration ends up resembling a hexagon with an additional coin at each corner. |
1 1 a b c d 2-3 2-3 e f g h 4 5-6 i j 4 k l m n o p q r s t u v w x |