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PostPosted: Sun Feb 19, 2006 2:14 pm    Post subject: Reply with quote

I believe the pattern in the post above is usually referred to as a BUG+1, to indicate that all cells except one have only two values while the exception has more than two. It's basically the last step before a BUG, which would lead to a puzzle with no or more than one solution.

In a puzzle such as this one, where the +1 cell has three candidates, it might be easier to think of it in terms of 'I need to place the value that appears three times in any row, column or block in the +1 cell', rather that 'I need to exclude from the +1 cell those values which only appear twice in the row, column or block', which, by default, places the same value referred to in the first part of this sentence.

I believe (but not positive) it is possible to have a BUG+1 grid where the +1 cell has more than three candidates. In that case there are two values that occur more that twice, which excludes simple placement of one of them and the values that occur only twice can be excluded from the +1 cell, which will lead to the solution.

David Bryant is correct about for what the acronym stands. I think someone, a drinker of non-American beer, also suggested Bivalue Universal Death (BUD), with the admonition to 'avoid the "BUD" at all costs', as an alternative name. I think it was intended in a humorous manner and was generally taken as such.
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PostPosted: Sun Feb 19, 2006 2:48 pm    Post subject: Different angle Reply with quote

Let me try to restate this.

(I think the people that came up with this were trying to be too clever. The acronym is silly, and it describes a pattern you wish not to reach.)

Maybe Binary Uniqueness Condition would be a better name?

If all the unsolved squares each have only two possibilities:

1. The puzzle has zero or two solutions.
2. Each possibility occurs twice in each row, block, or column.

Now, if you reach a situation where each of the unsolved squares has two possibilities, except one (the "target" square) has three possibilities: If the puzzle has a unique solution, it cannot be reduced to the state described above.

Look at the other squares in the same row, column or block. (It does not matter which you choose.) Two of the three possibilities will occur once in the other squares. The third possibility will occur twice, and this is the value that the target square must be.

Marty is correct: If three squares in the row, column, or block have possibilities XY, YZ, and XYZ, the value of the square with three possibilities must be Y. The values of the three squares are, respectively, X, Z, and Y.

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Marty R.

Joined: 12 Feb 2006
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Location: Rochester, NY, USA

PostPosted: Mon Feb 20, 2006 1:15 am    Post subject: Reply with quote

As always, thanks for the help.
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