Mathematical
Games and Puzzles
The stair-step diagram below contains seventy-eight cells with unique X and Y coordinate values. The objective of this puzzle is to fill as many cells as possible using three each of the 26 letters of the English alphabet.
Each set of three cells containing a specific letter must satisfy the
following coordinate conditions:
| X | Y | |
| cell #1: | x | y |
| cell #2: | x | v |
| cell #3: | v | y |
NOTE: Once x and y values are selected, v may be any value from x-1 through y+1.
After placing a letter in the three cells chosen, select another letter and proceed as before. An 'A' has been placed in the diagram below as an example to illustrate.
Questions: Is it possible to place sets of all 26 letters? How many can you place?
Idea for this puzzle is credited to Liang Haisheng of Osaka Japan.
This puzzle consists of a square board 36 units on a side and 36 tiles (size one through 8). The combined tile area equals that of the board (1296 sq. units).
Without overlapping, how many tiles can you fit on the board? Can you arrange all 36 tiles into a rectangular shape? There are 2,332 possible solutions not including alternate orientations of a given solution!
Martin Gardner first introduced this general type of puzzle in his 1992 book, "Fractal Music, Hypercards and More." At that time the solution was known for packing 78 tiles (size one through twelve) into a square 78 units on a side. The concept of "Packing a Partridge in a Square Tree" grew out of this analogy with the well known Christmas song. Later, this problem became known as the "Partridge Puzzle."
It should be noted that the mathematical relationship between board size and tile number is constant. In 1993, Charles Jepsen discovered a solution for a board size of 66 (tiles one through eleven). In 1996, Bill Cutler determined the smallest board size with a feasible solution forthis general problem was 36.
For further information regarding the Partridge Puzzle, other interesting games, or obtaining a Partridge Puzzle kit, please feel free to contact me: rtwainwright@iname.com
I am currently developing several packing puzzles and hope to have additional information pertinent to my work, as well as more links to more puzzle and game sites, posted here in the near future.
Recreation:Games:Puzzles- Yahoo sub-catagory.
Puzzle of the Week - Puzzles (logic, word, mathematical, etc.) posted weekly.
The Sphinx - Puzzles filed into various categories (e.g., logical, mathematical, etc.).