dailysudoku.com

[Glassman]

Uniquity is my term for the rather less than elegant situation of being forced to presume that a puzzle has a unique solution.

When I solve a Sudoku, I like to both obtain a solution, and prove that it is the unique solution. However, certain situations arise when solving a puzzle where you could use the knowledge that it has a unique solution to help solve it. The classic is a square or rectangular formation of four cells in two boxes, which uniquity indicates cannot contain just two numbers, as, if they did, the puzzle would have two solutions.

The really tough puzzle of Sun 26-Jun-2005 illustrates this. You can use uniquity to eliminate the 9s from r2c7 and r2c8, and the 3s from r4c3 and r5c3. To my relief the key to unlocking the puzzle is elsewhere, so you are not forced to use uniquity to help you solve it.

So far I cannot recall being forced to use uniquity to obtain a solution.

Any views on this? Or is it already fully discussed and documented?

Glassman

[David Bryant]

I can't recall ever using this idea to derive a final solution. If one did this, wouldn't it be necessary to test the possibilities that had been eliminated to be certain there weren't any other "solutions"?

I have used this idea to avoid mistakes. Just last week I made an error (assumed I could place a "9" when in fact I didn't have enough information to isolate it into a single cell).

I caught my error a few seconds later when I spotted a 4-cell rectangle that could contain only {4, 9}. That saved me a few minutes of additional work by helping me recognize my mistake before I otherwise might have. dcb

[Glassman]

[David Bryant]

You're right. Fortunately, Samgj hasn't let me down yet.

[David Bryant]

There's an interesting example of a puzzle with more than one solution right here in this forum. dcb

[Glassman]

David — It's an interesting example as it is more complex than a simple rectangle of four cells.

Glassman

[David Bryant]

[Glassman]

David — I have seen the word before, possibly in a large quantity of original mid 17th Century material I had through my hands relating to our Civil War. Fascinating and vitriolic material, easy to read once you get used to the blackletter print and the long s's, and very American in style, as your language has changed considerably less than ours. Which explains why my all-time favourite prose is Lincoln's Gettysburg Address, although it is not really prose but poetry, as you can hear the tune.

I reinvented it here as a portmanteau word, combining the iniquity of the compiler in forcing you to use uniqueness to solve the puzzle — but, as I said before, I have not yet been forced to use it.

Glassman