Tchuka Ruma Solitaire (UMAP)

The solitaire game "Tchuka Ruma" is described as follows in the book of mathematical diversions by Degrazia [1948, 102-103]: Tchuka Ruma is an East Indian game which can be played with the most primitive equipment, such as a number of holes and some pebbles. It may be mathematically analyzed, although its theory has not yet been fully explored. You have a board with five holes in a row. There are two pebbles (or pieces) in each of the first four holes, while the last, called Ruma, is empty. The object of the game is to put all the pieces in the Ruma hole in the manner prescribed.

Table of Contents:

THE GAME OF TCHUKA RUMA

WHY IS IT INTERESTING?

WHEN CAN YOU WIN?

VALUES OF k CLOSE TO n, OR LARGER THAN n

SMALL VALUES OF k

SMALL VALUES OF n
The Pattern for n = 1
The Sporadics
The Case n = 2

OPEN PROBLEMS

HOW MANY POSITIONS ARE THERE?

VARIATIONS
Tchuka Ruma without Wrapping
Two-Person Tchuka Ruma with One Hole

PROGRAMMING CONSIDERATIONS

APPENDIX: ANTHROPOLOGICAL DETAILS
Where Did It Come From?
Maybe from Egypt, Long Ago?
Maybe from Southeast Asia?
Games played by the Achehnese of Northern Sumatra
The origin of the words Tchuka and Ruma
Contemporary inquiries
Association of the game with wakes
Spiritual significance of mancala games
Or Maybe from Russia???
Our Conjecture

REFERENCES

ACKNOWLEDGMENTS

ABOUT THE AUTHORS