DanO wrote:I was going to file for a patent on the extended forms but the patent would be invalid if the form in not actually usefull

I think the next step is to see if we can come up with a generalized description.

Here is my first stab at it:

A

Unique Loop consists of a closed loop of naked pairs on the same number, traversing the rows and columns of the puzzle, with the additional restriction that each square in the loop is a naked pair in its block as well as its row and/or column.

Thus a Unique Rectangle is the simplest instance of a Unique Loop.

Assuming that that is correct, then:

In a

Type-1 Unique Loop, one of the naked pairs has additional value(s); in order to prevent a deadly pattern, that square can be reduced so that it only contains the original values.

This raises the questions:

* Are there Type-2 through -4 Unique Loops?

* Can the Unique Loop definition be extended; for example, instead of just one naked set pair (eg: the floor pair in Unique Rectangles) having extra values, perhaps more than one can in a Unique Loop?

* Is it possible to define Unique Loops where the base possibilities change around the loop?

I agree that Unique Loops are a special/rare form of forcing chains (so the answers are probably yes,no,yes) but they may be useful, in particular if something about their structure means that they can be embedded -- with more than 2 squares having extra possibilities.

I wonder if this qualifies as a unique loop:

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