Help for Deadly Patterns
 

This technique assumes that the puzzle being solved has a single solution, ie is unique. In general one can safely assume that this is the case. When there is a set of 4 cells forming a rectangle that spans two boxes, a special situation exists if it is possible find a solution where 2 numbers only are in these cells. If this is allowed to happen then a non-unique solution is obtained, because reversing the 2 numbers leads to a second solution. This is illustrated below:

    Type 1 Unique Rectangle.
In this first example, if the 4 in the bottom right cell is false, then each of the 4 cells contain "1,2" and two solutions are possible (1-2-1-2 or 2-1-2-1). Therefore the 4 must be true and both the 1 and 2 can be deleted from this cell.
 


    Type 2 Unique Rectangle.
In this example, if a 4 in a cell outside of the rectangle cells can see both the lower two cells of the rectangle, then if this 4 is true the the 4's in the recangle cells are eliminated and a deadly pattern of 1,2's results. Therefore the 4's outside thr rectangle can go.
 


        Type 3 Unique Rectangle.
In the left example, either the 3 in the lower left cell or the 4 in the lower right cell must be true to avoid a deadly pattern. The 3 and 4 thus form a virtual pair of numbers. If in the same row or box another cell contains the same two numbers, then we have a naked or locked pair, and eliminations can be made in the usual way (the red 3 and 4). In the right example, one of the 3 extra numbers in the lower 2 rectangle cells must be true, and if 2 other cells in the same row or box contain the same 3 numbers, we have the equivalent of a naked triplet (456, 45, 46). thus the 456 in the red cell can go.
 


        Type 4 Unique Rectangle.
In this type, there must be a strong link between 2 of the 1's or 2's. In the left example, if the 1's in the lower two cells of the rectangle are the only two in the row, then if the 2 in either cell is true, it forces the 1 in the other cell and the deadly pattern ensures. Therefore both lower 2's can go. Alternatively, if the 1's in the top left and lower left cells are the only ones in the column, then a 2 in the lower right cell forces the the top left cell to be 2, and the lower right to be 1. Therefore the 2 in ther lower right cell can go. The right example is the diagonal variation, but similar priciples apply.
 


        Hidden Unique Rectangle.
In the left example, 3 of the cells have extra digits, and on the right, all 4 have extra digits. In order to achieve a deadly pattern, the left example needs 2 strong links, while the right example needs 3. For example, in the right example say there are strong links of 2 in both of the columns, and a strong link of 1 in the top row. Then a 1 in the bottom left cell forces 2 in the top left cell, which forces 1 in the top right cell, which forces 2 in the bottom right cell. .
 


        Variant and Avoidable Unique Rectangles.
Variant URs have one or more missing deadly pattern digits. The example on the left is a Type 1. It is missing a 2 in the bottom right cell, but the deadly pattern still follows if the 3 is false. Variant URs come in type 2, 3, and 4 patterns, analogous to the regular URs above. The right example shows an avoidable pattern. Here, three of the cells are solved (NOT given). If 1 was true in the lower right cell, then a deadly pattern would result, therefore the 1 can be eliminated. .
 


    BUG-lites.
The simplist form of BUG-lite have 6 cells all containing the same two digits. They must be located in 3 boxes, 2 cells in each, with 2 of the cells in 3 rows, and 2 of the cells in 3 columns. This can occur as an "L" as in the example, or all six cells in a stack or a band. The example is a Type 1 pattern, but there are type 2, 3,and 4 types as above for regular URs. BUG-lites come in higher order patterns, not implemented here.
 


        MUG (Multivalue Universal Grave)
These deadly patterns are sometimes called MUGs because they have 3 digits rather than 2 (BUG = Bivalue Universal Grave). The examples show the 2 possible patterns, both examples being Type 1's. Again, like the regular URs above, they also come in types 2, 3, and 4.
 


Examples

Following are examples to illustrate these techniques. The majority were found in the Let's build a zoo ... thread, most contributed by Mike Barker. Many of the type 2 and type 3's are also type 4s, so duplicating my results depends on the order the different routines are executed. All the patterns follow directly after Basics are cleared, so clear Basics and then click "Deadly".

...1.49..7..9..42....7..6...6........2...5...8...3...4.8.....7....5.....231.6...5   UR Type 1
...658.....4......12............96.7...3..5....2.8...3..19..8..3.6.....4....473..   UR Type 1, then hidden(4)
.5........6.5.42....8.71...4....36.8.........89.1..7..3...........2.7.1..72.3..9.   UR Type 1, then Avoidable rectangle

.9...4...4..38........5.1.7..4...9.......9..3...2.3.64.8.........671.8.2..2....3.   UR Type 2
....9..27.3.1.78..6.....4....13.468..8...973...38..9..379...2.8...9.2.7.4527381..   UR Type 2
.7.9.3.8.....2....2..4.7..16.5...1.9.2.....6.7.8...2.59..2.5..6....7.....1.3.9.2.   UR Type 2, Diag, BUG-lite Type 1 (3 digit), hidden(3), Bug-lite Type 4 (3 digit)
..8..69.53..............6.......98..8...6.....561....354.3.........12.7..2..4.1..   UR Type 2
..9.7.6.4.326.....5.............5.....6.1.7.....4.............3.....752.8.7.6.1..   UR Type 2, then Type 4

............3..6......742...34.5.9.2.7.4..5.1.........8.5.16..36..........7.9...8   UR Type 3 (pair)
..7....4..2..67...9..4....1...3.1.....4.2.67.........8......35...5..9....3.6.4.2.   UR Type 3 (pair)
3.6.7...........518.........1.4.5...7.....6.....2......2.....4.....8.3.....5.....   UR Type 3 (pair)
..........9..86.7...1..2.9..2.9....8.......5..4627...9..5...8....8.1.7..2..4.....   UR Type 3 (pair)
..9.35.....6...1.8.2.1....5..4....72..1.9...6......4...7..84.....5.73..16..21....   UR Type 3 (pair)
...9....4......5..76..8....2.....1....12.9..5..471.9.21...4......7.258.1..21.....   UR Type 3 (pair) x2
6.7.8.5.3.9.....8.4.......6...4.....5..2.1..49....3..83.......7.......6.7.5.1.8.9   UR Type 3 (pair), then Type 1, then Type 4, then Variant Type 4
.........6..7..5.9.8954..7.2....1.57...374...76.2....3.7..9823.8.6..2..4.........   UR Type 3 (triple), then Type 4 x2, Diag, Hidden, BUG-lite Type 4

....1.2....6.....7.....436..8.1.....4.29.3...9.3.......3.8.2.455......7.6..3..8..   UR Type 4
.....2..4..17..8...4..6..3.4.6.....53.7....8......9.....9.18..21......5..5...476.   UR Type 4 x2
53..2.9...24.3..5...9..........1.827...7.........981.............64....91.2.5.43.   UR Type 4 x2
...5.1..32.9..48...4....5...1.96......2...1......17.8...8....2...34..7.65..7.9...   UR Type 4, then Type 3 (triple)
.78....1.5...4......6.72...85.........45.79.........64...18.2......6...1.1....35.   UR Type 4 x2, then Type 3 (pair)
4.......6...1.9....3.4.59...9.2.1.8...1.5.2...7.9.4.1...65.2.7....3.8...9.......8   UR Type 4 x2, then Hidden(3), then Type 3 (pair)(from SudokuWiki)
...7.4.....1.8.7...752.381.9.4...3.5.6.....4.5.7...6.9.428.793...8.3.4.....4.1...   UR Type 4 x3, then variant Type 4, then BUG-lite (x2) (type 4, type 1, 3 digit)

2.1.....8.....3..........626.3..7....52.947..7..3..1..4....6.519..5...4...7.1....   UR Hidden(3), then variant Type 4
.5946..122.......6.1...9..7...12.5..5..........4..8......68......2.5.7.8.9....3..   UR Hidden(3), then Type 3 (pair)
14..3...........6....845....2.....9..18......9.6....78.5.7..9..372.1...4..4.....2   UR Hidden(4), then Diag, then Hidden(3)
...5...........5.697.....2...48.2...25.1...3..8..3.........4.7..13.5..9..2...31..   UR Hidden(3) (x2), then Type 4
.....7.4.3.....82.4.8.....57.3.2.98.2...9...6.4.16.7.......2.9...6..9...19.......   UR Hidden(4), then BUG-lite type 1 (2 digit)
7.......2.9.......8..9..1.7..94.3....2.6..38..5.21..4.915...4......2.5......6...8   UR Hidden(4), then BUG-lite type 3 (3 digit - pair)
.3...52.42...8...1........869.5...3......4..........9..85.7...93....6....4..2....   UR Hidden(3), then Type 4, then variant Type 4
..2.9......46.7....9...43..7.8.....9.4..2.8...5..3.1.....5.......6..89.........37   UR Hidden(3), then variant Type 4
........8.....863..9.13.4...473........51..9..........62.8...1..78.....5...6258..   UR Hidden(3), then variant Type 4
..5...82.1...94...3..25....52...1......5...48...4..23....61...7.13...5..26....4..   UR Hidden(3), then Type 1, Hidden(3), Type 4, then Variant Type 1 (x2)
...9.3..42..6.89.........7.48.7.9.13....8....91.5.2.87.5.........31.7...6..3.4.9.   UR Hidden(3), then Type 4, then Diag (x2), then Variant Type 1
63......4..5......74..3..6..2.4.5........19......6...7..4.2..9.25.9.8......5..1..   UR Hidden(3), then Type 1, then Hidden(3) (x2)

.7.2..3..6.21..45.....7...8....6...4...8.7...5...3....7...5.....69..87.5..5..3.6.   UR Diagonal, then Type 4
.....68.5.....1.67..4.5.........7..3.6..1..4.5..2.........9.2..91.5.....8.73.....   UR Diagonal, then Hidden(3), then variant Type 4
.1.9..76.6..2.....9......25..6..2.83.....7....3..6.1.........1...74....8.8..5..79   UR Diagonal, then Hidden(3), then variant Type 4
...........43526...7.....5..3...8.9..5..3..7..2..7..4..8.....1...76498...........   UR Diagonal, then variant Type 4 (x2)
.2.5...74.73......4.....5.39..2..3...4..9..6...8..4..18.5.....6......23.71...3.9.   UR Diagonal, then Type 3 (2 digit)

..8...2..9.......72.7....934...9...6....2.........31.5.....8....5.43.....6...7.84   BUG-lite type 1 (2 digit)
........4.1..2..35..3..51..7.1...3..8....6.........7.695..78.2..7..9........1..8.   BUG-lite type 1 (2 digit)
1...4....2.8....19...98.7...6.......89...7.....7.13.....6......72....4.....2...86   BUG-lite type 1 (2 digit)

.....1.54.9..3.2..374.....1....2..8.5.946....2.8.1.......9......4.6...1...6.....5   BUG-lite type 1 (3 digit)
147.5.......9.......8......4.........8.7..36..6..4.5.9.3.6..........4792....281..   BUG-lite type 1 (3 digit)
3.....4...14.67.....9..2.16.3...894.....5.....926...7.62.9..7.....27.68...8.....2   BUG-lite type 1 (3 digit)

24..5..899..4.8..5..8...3...8.527.3.4..3.6..7.3.849.5...2...9..8..9.5..219..8..73   BUG-lite type 2 (2 digit)
3.....4.........8..9..4.1.........7...8..6.....4.796...7.9.83...4.32....25...1...   BUG-lite type 2 (2 digit)
.4.7...6..13....4.7..14......8..7..347...6..9........73.5.........29....9..4..31.   BUG-lite type 2 (2 digit)

..8.....693.....2..62.1.9...8.9.27...7.....9...97.6.1...7.5.46..9.....351.....8..   BUG-lite type 2 (3 digit)
...9...756...8.........19.....34......1......87......2.9...7.....7...46...3..5.91   BUG-lite type 2 (3 digit)
1.2.....3.45.....1.6....752...826...............495...527....3.3.....69.8.....2.5   BUG-lite type 2 (3 digit)

.8....25..6.8...4.9...24..3..6..8.....71..5.....5..9.1.2....3....9......35...28..   BUG-lite type 3 (2 digit - pair)
.4..1.3..8..3.....2.....5....913.....6.9....5.....7..2.....4....8.65..4.72....1..   BUG-lite type 3 (2 digit - pair)
54...6.....945.3....1...9...2.3...4.8.5..9..1......2.......5.1...6..2.3..7.......   BUG-lite type 3 (2 digit - pair)
.1.......46.3....5...9..2.6.8..4..............2...1687..56....81.......99...8..7.   BUG-lite type 3 (2 digit - pair)
.....9.86.56.1........5.....8.29..4.....4...137....2..19...5...7........8.2.....4   BUG-lite type 3 (2 digit - pair)

...4...1.23.....4....3.6.9....9.........8..217.........5......73..72.48...285....   BUG-lite type 3 (3 digit - pair) 
.6......239.6...17..5...........67.8...5....148.13........524..9..3......5..1.27.   BUG-lite type 3 (3 digit - triple)

...13.8..29.........6..4.2...5.......19.....27......4...8..15...6.7...3.5..8.32.1   BUG-lite type 4 (2 digit)
.51...6.9........8...4..57.....96.2.2.......3...8.......427...1..5.49...9.....7.5   BUG-lite type 4 (2 digit)
...1..4...7...48.....8..7.3.96.8........9..1...756.....4.......16.9.3....5..1...2   BUG-lite type 4 (2 digit) x2  
...3....5..2..7.4.6.1......8..72..9.4....936.......4...8....2..526.8.....7...6...   BUG-lite type 4 (2 digit) x2, then BUG 
...1....9..6..2.8.7.3......5..26..4.8....417.......8...5....6..967.5.....2...7...   BUG-lite type 4 (2 digit) x2, then BUG 

..63..8.52...8.......5....237.8...41.....1...1...9.2...........58.2..3.......64.7   BUG-lite type 4 (3 digit)
..4...18..6...7.3...1.........34.5.69..5...7.......9.......3..85..2.....8.3.6...2   BUG-lite type 4 (3 digit)
.9..8..7....3...5265.4.....8.7..31.61........9..8.4.......6.4.778..........2.....   BUG-lite type 4 (3 digit)
5...7.682.2.......87........9..8..4.3....9....8..1...66....3..173..9...........65   BUG-lite type 4 (3 digit), then BUG-lite type 3 (3 digit - triple) 
1...6.....8.5.7....6..8.3.....9..23.2...14..........967.6.....4.......1..9.2.6..7   BUG-lite type 4 (3 digit), then Diag UR, then BUG-lite type 1 (3 digit)
...4....3..4.258....2..8..7.7...........51....49...2.....3......2..4.5.68...6.7..   BUG-lite type 4 (3 digit), then BUG 
...1.3..........986...97...........6.5....839....84.2...8......196.....2.2....47.   BUG-lite type 4 (3 digit), then BUG

....126.7.59....32.......8.7..........84...7...58.912..9.7582....6.4...5.4.......   Classic BUG+1
....1.4........936....345..8579..........218..6...........7.32.4.31.5...2........   Classic BUG+1
1...6....6..8....5....52....9....4.886.....9......3.1.7.2.4..6....5.83...5.......   BUG+2
.6..98.4.31.......5.8....3...1..6.........4.....1825.....245..7...9..6.1..7...2..   BUG+2