1Definition: Four cells in a rectangular arrangement following the same rules as a Unique Rectangle: occupying exactly two rows, two columns, and two blocks. Two or three of the cells must already be solved, and none of them can be a given. (Note that in Sue given numbers are shown in black, cells that have been solved -- by you or by Sue -- have blue numbers.) To make the puzzle unique, these cells cannot resolve to just two numbers. To avoid this possibility erasures can be made.
Avoidable Rectangle (yellow cells) G6 cannot resolve to a 6 in a puzzle with a unique solution.
2Look For: Take a look at our example: four cells in the UR pattern, with no givens. The three solved cells in the pattern only contain two different numbers: 3 and 6.
3Consequence: The unsolved cell G2 must contain something other than a 6 in order to avoid ambiguity, so the 6 can be erased from this cell (leaving it to resolve, in this case, to a 9).
4Why it Works: If there were only two different numbers in cells of the UR configuration, the numbers would be interchangeable, and the puzzle ambiguous. In our example, if G2 were a 6 the 3's and 6's would be interchangeable, resulting in more than one solution for the puzzle.
5When there are only two solved cells in the pattern, as in our Type 2 example, the erasures (if any) occur outside the AR cells. Here, the unsolved cells are B6 and C6, one of which must be something other than 5 or 9 to avoid ambiguity, which means one of the unsolved cells must be a 6, so cells which see both unsolved AR cells can have their candidate 6 erased.
The AR is in cells B5, F5, B6, and F6. One of the unsolved cells will have to be a 5, so any cells that see both F5 and F6 can have their candidate 5 erased.
7Excellent! The solution was to erase the 5's in F2, E5, and E6 (since they can see the unsolved cells of the AR, one of which must resolve to a 5 to avoid ambiguity).
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