Among the many solutions received, the only correct solutions were submitted by Juan Carlos Marivela, Lou Cairoli.

There are 288 Sudoku Jr. puzzles.

We first make a couple of simplifying reductions.  

• Interchanging all occurrences of one number with another in a valid Sudoku Jr. puzzle yields another valid Sudoku Jr. puzzle.  

• Interchanging the first two rows of a valid Sudoku Jr. puzzle yields another valid Sudoku Jr. puzzle; the same is true when interchanging the last two rows, the first two columns, or the last two columns.  

Applying appropriate interchanges as needed, we can assume that our Sudoku Jr. puzzle starts as Puzzle A.  Right away, the (3,3) entry must be a 4, putting us at Puzzle B.  Trying the number 2 in the (2,3) entry leads to a quick contradiction. With a 1 in the (2,3) entry, there are two valid puzzles, C and D below, and with a 2 in the (2,3) entry there is only one, E below.  

Therefore there are 24·2·2·3 = 288 valid Sudoku Jr. puzzles. 

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©2005 Alberto L. Delgado