Type in either your index or your SUDOKU solution, and press the submit bottun; then the program will give you the answer in 15 sec.

From SUDOKU Index to SUDOKU solution

From SUDOKU solution to SUDOKU Index

SUDOKU Index

Introduction

B. Felgenhauer and F. Jarvis (2005) succeed to count all SUOKU solutions and showed that there are about 6.67 x 10**21 valid solutions. Based on their technique, we succeeded to give an index to each of these SUDOKU solutions and to make a program that gives this index from a given SUDOKU solution efficiently.

You can try this program in this page; both from index to solution and from solution to index. The program runs in about 15 sec. Please try it!

Remarks:

1. SUDOKU (SU = number, DOKU = single), a general name "Number Place", is a trademark of NIKOLI.
2. SUDOKU considering here is the standard one for the 9x9 grid.
3. Please refer to this index the FJTW Index, abbrv. for the Felgenhauer-Jarvis-Togami-Watanabe Index.

Our Method

Due to the huge number of possible SUDOKU solutions, it takes enourmous time to go through all solutions for indexing. Furthermore, we need huge amount of memory space to keep all solutions to provide a fast indexing program.

Felgenhauer and Jarvis (2005) classified all 36288 classes of cannonical SUDOKU sokutions into 71 equivalent types, thereby couting all SUDOKU solutions. We essentially followed (*1) their method and made a database of solution search trees for each of these 71 types. And we could reduce this database size to 4GB. Based on this database, we could design our indexing program with running time about 10 sec.

*1 We could reduce the equivalent types from 71 to 67 by introducing one more transformation rule.

Links

1. Sudoku enumeration problems Dr. F. Jarvis's page for his papers and programs.