confined to two intersecting houses.
Depends on how you view the intersecting houses:
Directly with an shared cell "hinge" as seen in most of the typical wings that primarily composed of Row/Col + Box and expressed to form all the â€œwingsâ€ seen up to this date.
However box - box for smaller ones will also work using peer line of sight as a reference to connect the cells.
For example:
b1 = xz, b2 = xy, xz => R3C123 <> z
- Code: Select all
| . yz . | . . . | . xy . |
| . . . | . . . | . . . |
| -z -z -z | . . . | . . xz |
The first one with an interesting double linked elimination occurs when N=4.
Viewed as a cover problem for box + box operations
where the digits used in both sets are the same digit set:
B[A] contains ( x ) cells with ( N+1 ) digits
&
B[B] contains ( x ) cells with ( N+1 ) digits
where B[AB] = (N+1)
b[A] = box for group of cells, where A represents those cells. {total # of active cells are counted}
b[B] = box for group of cells, where B represents those cells. {total # of active cells are counted}
B[AB] represents the total count of all active cells and there respective positions from B[A]+B[B].
then the sum of the two active boxes = (N+1) digits.
if a cell in B[A] is peer to a cell in B[B] and that cell in B[AB] share 1 or more
digit(s) then all common digits are a restricted link {RL}
Digits locked with in either box is a restricted common {RC}
All cells that are peers of cells within B[AB] < > any other digit in B[AB] that is not restricted to the B[AB] cells
Using the above example of a xy-wing I find a B[A] with 2 cells and B[B] with 1.
B[A] = R1C1 {yz}
B[B] = R1C7 {xy}, R3C9{xz}
RL{restricted link} Y
RC {restricted commons} X
= > R3C123 <> Z
When increase the N = 3 digits you have several formations that can occur for groups of 2 boxes specifically
Case 1: {eg Types: 2, 2a, 2b, 3, 3a, 4, 4a,}
B[A] with 3 cells & B[B] with 1 cell
Case 2: {eg Type: 1b} & [purposed new type double linked]
B[A] with 2 cells & B[B] with 2 cells
Case 3: {eg Types: 2, 2a, 2b, 3, 3a, 4, 4a,} {inverse of case 1}
B[A] with 1 cell & B[B] with 3 cells
With the same formula with the type I purposed earlier
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| . wxz . | . . . | wy . . |
| xz -xz -xz | . . . | . xyz . |
| . . . | . . . | . . . |
B[A] = R1C2 {wxz}, R2C1 {xz}
B[B] = R1C {wy}, R2C7 {xyz}
RL = W
RC = Y
= > R2C23 <> x,z
edited to correct typos and add clarification: