The New Sudoku Players' Forum

[RyanStorm]

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[JasonLion]

If you have a pair (two cells in the same house both of which can only contain the same two digits) you can't have those two digits anywhere else in that same house. A house is a row, column, or box.

In you first example, the pair on 47 eliminates 4 & 7 from all of the other cells in that column, but doesn't tell you anything about the 37, which is not in the same column.

[eleven]

RyanStorm,

note that both the 47 box in the 1st and the left 47 box in the 3rd row could be 4 in your first picture. So the 7 in the 37 box is still possible.

But your picture shows a "remote pair" pattern.
If the box with 4 or 7 in the first row is 4, then the one in row 7 must be 7, and vice versa, if the one is 7, the other is 4.
That means, that (taking the row/column numbering of the second picture) the box in row 7 and column 9 cannot be 4 or 7, because 4 and 7 are in these 2 boxes, in the same column or row resp.

However we cannot see, if this would help you in this puzzle.

[RyanStorm]

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[RyanStorm]

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[daj95376]

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My solver treats a Remote Pair as two XY-Chains using the same cells. (see below)

Code: Select all

 +-----------------------------------------------------------------------+
 |  234    24     5      |  9      37     8      |  1      6     a47     |
 |  34     7      9      |  34     6      1      |  5      2      8      |
 |  1      8      6      |  2      5     c47     |  3     b47     9      |
 |-----------------------+-----------------------+-----------------------|
 |  9      126    7      |  5      24     3      |  8      14     246    |
 |  268    1256   3      |  78     2478   69     |  2679   14579  24567  |
 |  268    256    4      |  1      278    69     |  2679   579    3      |
 |-----------------------+-----------------------+-----------------------|
 |  7      46     2      |  34     39     5      |  69     8      1      |
 |  45     9      8      |  6      1     d47     |  27     3      25-7   |
 |  56     3      1      |  78     789    2      |  4      579    567    |
 +-----------------------------------------------------------------------+
 # 65 eliminations remain

 RP (7=4)r1c9 - (4=7)r3c8 - (7=4)r3c6 - (4=7)r8c6  =>  r8c9<>7
 RP (4=7)r1c9 - (7=4)r3c8 - (4=7)r3c6 - (7=4)r8c6  =>  nada


However, you are now stuck on where to go after the Remote Pair. There are two choices that I would recommend.

(1) Look for other XY-Chains present. Especially those that contain a <4> in the starting cell.

(2) Learn about "Fish" patterns. There are several for <4> and <6> that crack your puzzle.

Spoiler: Show

Code: Select all

 XY-Chain: (4=3)r2c1 - (3=4)r2c4 - (4=7)r3c6 - (7=4)r8c6  =>  r8c1<>4

 Fish:     (4)r2c4 = r3c6 - r8c6 = (4)r8c1  =>  r2c1<>4


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[RyanStorm]

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[RyanStorm]

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[RyanStorm]

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