It was probably inevitable: Sudoku has managed to find its way into the world of Wiibrew, as it did in PSP and Nintendo DS homebrew. Sudoku for the Wii comes from developer dlkj, and comes with a number of features, including the ability to save the game on your SD card. Here's the readme for Sudoku v0.1a from the download archive:

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What's new
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0.1a:
- initial version.
- supports wiimote
- auto checking for validity
- single save game feature
- possible to mark 'uncertain' cells

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How to play
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hold the wiimote sideways
[+ : 00]
digital pad : move cursor
1: decrement
2: increment
A: mark uncertain
+: reset puzzle
-: save game to SD card
home : exit

red tint on incorrect tiles.
gray tint on uncertain tiles.

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TODO
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- various difficulty levels
- hint system
- menu system