"Many number" in Japanese could be "Su Ta" or "Su Shuu".
But like Pi I don't think that's a relevant name for the "sudoku puzzles with multiple solutions". My personal opinion is that the Japanese puzzle solving public has a strong belief that decent puzzles should only have unique solutions, so giving a Japanese name for that particular concept is utterly inappropriate.
My suggestions would be "pseudo-sudokus" or "imperfect sudokus"...
And like many others I'm expecting Dan/Fleury to post his alternative solution to the 2nd "diabolical" puzzle, which is rated "easy" according to my program... ^_^