# Introduction

I found the axiom of sudoku rules. The axiom was named "UMEKICHI". We can arrive at a theorem of standard sudoku rules by using UMEKICHI.

If sudoku rules was "Special theory of relativity", UMEKICHI is "General theory of relativity". Theorem of standard sudoku rules is contained in UMEKICHI.

# Body

I present the axiom here.

# UMEKICHI

1. Prepare a grid-based puzzle board like chess board.
2. The board size is determined for each puzzle.
3. Put one of the numbers given in empty cells.
4. Each number has a role that is one kind of chess pieces.
5. If there was no other numbers, no number attack to same number each other.
6. When board has some blocks of any cells, numbers can not repeat on each block.

Annotation:
• Numbers may be represented by any identifiable symbols.
• Having a block is an option for each puzzle.

We can arrive at rules of standard sudoku and other puzzles by using UMEKICHI.

# Example 01: Standard sudoku

1. Prepare a puzzle board sized nine rows and nine columns.
2. Put one of the numbers given in empty cells.
3. Each number has a role of chess piece "Rook".
4. If there was no other numbers on puzzle board, no number attack to same number each other.
5. The board has nine blocks sized three rows and three columns, numbers can not repeat on each block.

A standard sudoku is also paraphrased "Rook Place".

# Example 02: Yazhime (original puzzle in UMEKICHI project)

1. Prepare a puzzle board sized eight rows and eight columns.
2. Put one of the numbers given in empty cells.
3. Each number has a role of chess piece.
(1=queen, 2=rook, 3=bishop, 4=king, 5=knight, 6=pawn).
4. If there was no other numbers, no number attack to same number each other.
5. Board has no blocks.

You can see the puzzle example at Android App "Yazhime"

# Example 03: Skewdoku (original puzzle in UMEKICHI project)

1. Prepare a puzzle board sized nine rows and nine columns.
2. Put one of the numbers given in empty cells.
3. Each number has a role of chess piece "Bishop".
4. If there was no other numbers, no number attack to same number each other.
5. The board has nine blocks sized three rows and three columns, numbers can not repeat on each block.

You can see the puzzle example at Android App "Skewdoku"

# Example 04: Queen Place (original puzzle in UMEKICHI project)

1. Prepare a puzzle board sized seven rows and seven columns.
2. Put one of the numbers given in empty cells.
3. Each number has a role of chess piece "Queen".
4. If there was no other numbers, no number attack to same number each other.
5. Board has no blocks.

You can see the puzzle example at Android App "Queen Place"

# Conclusion

Standard sudoku and other puzzles seem to completely different. But We can arrive to their rules by UMEKICHI. Amazing. Therefore, UMEKICHI contains theorem of standard sudoku rules.

Quod Erat Demonstrandum.

January 08, 2014
Stew Eucen
facebook article for proof the date