A
B
C
D
E
F
G
H
I
1
6
2'
3
5
7
9
1'
3
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8
1
2
2
3
7
2'
3
8
7
8
6
4
1'
3
1
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5
9
1
2
5
3
1
4
9
8
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2
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7
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4
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4'
5
7
2
1'
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9
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6
1
4
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5
3
4'
9'
3
6
1'
6
1'
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5
1
3
9'
2
8
6
3
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5
9'
3
5
8
1'
8
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4
2
6
1
3
5
9'
3
4
7
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8
1
3
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6
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9
8
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7
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9
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8
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9
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9
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8
1
6
XY-Chain Technique
1Definition: An XY-Chain is similar to an X-Chain except that it involves more than a single digit. The chain switches digits on every strong link. The switches are all made within BVCs. These are strong links because BVCs only contain two candidates. The weak links (or surrogate weak links) occur between cells, and are always from and to the same digit in both cells.
XY-Chain starting and ending with strong links on digit 3. Alternating strong/weak links with all strong links being within BVCs. Cells seeing both end-points can have matching digit erased.
2Look For: BVCs in the same house that share a digit, which can be linked together via a chain alternating between BVCs (the X in the name) and within BVCs (the Y in the name). You may want to first find two BVCs that share a digit but not a house, and find the shared digit in another cell that can see both of these BVCs (i.e. find the end-points of the chain, and the potentially eraseable digit that sees both of them). Then you can try to build the chain between these BVCs, with a strong link from the first digit and a strong link to the last digit.
3Consequence: Any cell that can see both end-points of the chain can have its digit that matches the starting/ending digit erased. In our example the end-points are A2 and B5, with digit 3 being the strongly linked starting and ending digit. The cells that can see both A2 and B5 are B1-3 and A4-6. So, we can erase all 3's in these cells.
4Why it Works: This works for the same reason other chains work: each digit of the same color will share the same logical value (true or false) due to the alternating strong and weak links. With the end-points being strong links to the same digit, we know one of those cells will be true for that digit. Therefore, any cells that see both end-points cannot contain that digit.
5We have seen XY-Chains before, on a small scale with XY-Wings.
6Your Turn!
Find a productive 7-link XY-Chain in this puzzle. Then find the cells that can see the both end-points of the chain.Erase the matching digit from those cells.
Hint
Find a productive 7-link XY-Chain in this puzzle. Then find the cells that can see the both end-points of the chain.Erase the matching digit from those cells.
Hint
The starting/ending digit of the XY-Chain is 9.
Another Hint
Another Hint
You can start the chain at I1, then link to B1... ending up at the endpoint on F2.
One More Hint
One More Hint
The links are: I1 (9-4), B1 (4-5), B2 (5-2), F2 (2-9) Erase all the 9's in cells that see both endpoints (there are 5 of them).
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