rillian
Solution?
This is a top view, showing the little tiles used for guesses - or in this case to raise the large tiles up to show the decisions made. Also clearly shown is how the tiles are balanced on edge, when further decisions needed to be made. The tiles made it easy to show the decision tree, and to backtrack when necessary when a block occured.
The initial conditions were taken from one of the hard puzzles taken from the book that came with the sudoku tiles. In the 2nd and 3rd rows from the top, and the 2nd and 7th columns from the left are 4 squares left blank. They form a closed group - each square needs a 1 and 6, and once one tile is placed in one of the 4, the rest fall into place, but right now the solution to the sudoku is not unique. Despite this, the rest of the solution differs quite a bit from the solution in the book. I can't find any errors in this solution, which leads me to the conclusion that the initial conditions used for the puzzles in this book weren't well checked for uniqueness. It's quite easy to set up a sudoku which isn't unique. The challenge, of course, is to make the initial condition such that the answer is unique (or close to unique).
The carefully set up board was safe for about 12 hours, until an errant toe jiggled the box.
Solution?
This is a top view, showing the little tiles used for guesses - or in this case to raise the large tiles up to show the decisions made. Also clearly shown is how the tiles are balanced on edge, when further decisions needed to be made. The tiles made it easy to show the decision tree, and to backtrack when necessary when a block occured.
The initial conditions were taken from one of the hard puzzles taken from the book that came with the sudoku tiles. In the 2nd and 3rd rows from the top, and the 2nd and 7th columns from the left are 4 squares left blank. They form a closed group - each square needs a 1 and 6, and once one tile is placed in one of the 4, the rest fall into place, but right now the solution to the sudoku is not unique. Despite this, the rest of the solution differs quite a bit from the solution in the book. I can't find any errors in this solution, which leads me to the conclusion that the initial conditions used for the puzzles in this book weren't well checked for uniqueness. It's quite easy to set up a sudoku which isn't unique. The challenge, of course, is to make the initial condition such that the answer is unique (or close to unique).
The carefully set up board was safe for about 12 hours, until an errant toe jiggled the box.