Sumodoku
by Henry Kwok

Players:   Two.

Start:   Each player gets the 9 pieces of four different colors, plus 4 pieces of the ninth color. The one remaining piece is set aside and will not be used except in a special situation as the fifth way of winning the game (described below).

Play:   Each player takes turns placing one piece at a time on any unoccupied space of the 9x9 grid. Pieces need not be adjacent.

Rules:   As in standard Sudoku, no two pieces of the same color are allowed to be placed in the same row, same column or the same 3x3 box as marked on the board.

If a mistake occurs and a duplicate color is played where neither player notices and a third-party observer points it out, simply remove the offending piece from the game, with a hole remaining, and the game continues. You may, however, fill the hole with another piece later if the piece is an allowed color.

Win:   There are five ways to win the game:

1. The player who first plays out all 40 pieces wins. This is a very unlikely occurrence!

2. The last player able to make a valid move wins.

3. The player loses who makes an invalid move and the other player points it out. However, a move is not final until the player’s hand lets go of the piece.

4. If a mistake occurs such that a duplicate color is played, but neither player notices it at first, the player who first finds the mistake wins.

5. After both players have had 15 turns, so that there are 30 pieces on the board, both players on their turn have the opportunity to fill in all the remaining spaces by shouting “Sudoku!” (just as a chess player shouts “checkmate” in chess).

   Besides the spare piece, the contending player will get all the remaining pieces from the other player. With all the pieces at his or her disposal, the player will win by placing all the pieces correctly to form a valid Sudoku puzzle within the time limit of 16 minutes.

   The players will have to think very carefully before deciding whether to grab the chance to form a valid puzzle by themselves, because one or several pieces may be in the wrong position, even though placed according to Sudoku rules. Once a player seizes the opportunity to solve the whole puzzle alone and then finds that the puzzle has already been rendered impossible somewhere by one or both players in the first 15 moves, that player loses.

   If neither player grabs the chance to solve the whole puzzle by the 16th move, each player still retains the option until the 35th move. This means that after the 35th move (70 pieces), neither player may fill in the remaining 11 spaces single-handedly.

   There is a time limit for a player to finish a valid puzzle with all the remaining pieces. The time limits are as follows:

   • From 16th to 20th moves — 16 minutes
   • From 21st to 25th moves — 12 minutes
   • From 26th to 30th moves — 8 minutes
   • From 31st to 35th moves — 4 minutes

   If the player does not finish in the allowed time, the player loses.

Variations:  

• Instead of assigning colours to each player, on a turn a player may choose any colour to play.

• Both players may choose to form a Sudoku X puzzle by agreeing on an additional rule that each of the two main diagonals of the 9x9 grid must contain the 9 different colours.

• Both players may choose to form an odd/even Sudoku puzzle by agreeing on an additional rule that certain squares of the 9x9 grid should be filled either with odd or even numbers. In this case, they need to agree on which colours should represent “even numbers” and which should represent “odd numbers”.

• Both players may choose to form a consecutive/non-consecutive Sudoku puzzle by agreeing on an additional rule that certain squares of the 9x9 grid should be filled either with consecutive or non-consecutive numbers. In this case, they need to designate the digits 1 through 9 to each of the nine different colours.