## Making a puzzle harder by adding a number

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

C
coloin

Posts: 1737
Joined: 05 May 2005

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.
Some do, some teach, the rest look it up.

StrmCkr

Posts: 861
Joined: 05 September 2006

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