Making a puzzle harder by adding a number

Everything about Sudoku that doesn't fit in one of the other sections

Postby coloin » Wed Sep 10, 2008 7:08 am

StrmCkr wrote:if a postion of cells is alinged to form a pattern known as mutiple solutios is lacking a cells to complete the pattern can a cell be "temperorarly" removed.

This pattern is termed an "unavoidable set" and if a proposed solution grid has this set it would need a clue in it. As it doesnt have a clue in it - this solution grid cant be the solution to the puzzle.

coloin wrote:StrmCkrs question perhaps should be "Can we take a minimal puzzle, remove a clue and then find a UR. [A UR which wasnt there before and doesnt envolve the removed clue]

The 9@r2c6 is envolved in the UR. It cant be used.

But if a distant UR was revealed then this might give an elimination. How this would happen I dont know, however.

Maybe look in hard puzzles with > 30 clues

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Postby StrmCkr » Wed Sep 10, 2008 10:33 pm

But same for the 6 in r3c9. If it would not be given, you could eliminate 6 from r6c8. But this is part of the solution.

That shows, that you cannot temporarily remove a given, make a uniqueness based elimination and reinsert the number then.

ah yes i see it.

but it does give some forseight as to which number it is when reinserting the clue back in using a chain of some kinds:)

the removed clue becomes the only valid answer. via contradiction chain off that number that was excluded.
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