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# Cage Comparison

Documentation to be done

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## ... by: JohnNoneDoe

Original killer sudoku:

https://www.sudokuwiki.org/killersudoku.htm?bd=121221121121334421244441221222121334333124444222121224233331331121224431121331131,0808100700130024130000001700060000001924000000040000000000001815001300261600000000000000001900000000061300000026000
00000140019080807120017000000000000030012000000

Using only strategies 7 and 15 the solver produces:

https://www.sudokuwiki.org/killersudoku.htm?bd=121221121121334421244441221222121334333124444222121224233331331121224431121331131,080810070013002413000000170006000000192400000004000000000000181500130026160000000000000000190000000006130000002600000000140019080807120017000000000000030012000000

The solver cannot proceed further even with all strategies enabled.

Consider the cage starting at d5 and the 1-cell pseudo-cage b5; the cage at d5 cannot be 189 because that would leave b5 empty. Solution is straightforward if the 1's are removed from cage d5.

## ... by: JohnNoneDoe

Here is another board which thwarts the solver.

There is a Killer Sudoku board I would like you to look at

http://www.sudokuwiki.org/killersudoku.htm?bd=112212212223313412112213413113313443124412241322313311312312211212313322214412211,060012004508000812090009000015270000240017000000000013000003000000000000002706000013000022140000170006000000001600000013000000080000000009001300000012000009001200

The solver fails but the puzzle is easily solved using cage comparison.

The 12-in-2 cage at ab9 must be 9,3 or 8,4. Thus the 8-in-3 cage at abc8 cannot be 1,3,4; it must be 1,2,5 and the solution is straightforward

## ... by: JohnNoneDoe

There is a Killer Sudoku board I would like you to look at

http://www.sudokuwiki.org/killersudoku.htm?bd=112212211231111123233444223133121221122121331212121312212312312414312414444414444,080015002507001300062300000000002014000000190000000000080000151317000011002200000000200000131700000000001703000000091609000000270000000000380000000000000000000000

The solver fails on this board. It can be easily solved using what I think is an application of cage comparison. The 13-in-2 cage at a78 cannot contain 6,7 because of the 15-in-2 cage at a34. Thus the 5 cell innie in box 3 summing to 45-13-14=18 must contain a 7, 18-in-5 is 12357.

## ... by: JohnNoneDoe

Below is a board that thwarts the solver.

There is a Killer Sudoku board I would like you to look at

http://www.sudokuwiki.org/killersudoku.htm?bd=112212211213313312244212442114232411112131211232121232231121132132232231111333111,190009001808001700100006000012000005001500070006220000200000001100002100000015270018070000051100000600001814000000000000000000190009002511000014000000000000000000

The solution is straightforward when one notes the hidden pair 1,4 in 5hj and 5fg which leads to a hidden pair 8,9 in 5abc and 6b. I think think this observation would be a result of what I think of as cage comparison.

## ... by: JohnNoneDoe

I am looking forward to the cage comparison documentation. I assume it covers such things as 5 in 2 and 6 in 2 in the same unit, seems very powerful.

## ... by: Thinkist

If I'm understanding correctly, this strategy is the exact same as Killer Combinations (hard).

Also, the X-Wing strategies and those below it are useless (or at least really rare). Same for KenKen and KenDoku.

Article created on 7-August-2011. Views: 20982