On a star system, this would probably be 4-5

Perhaps one or more of these variants have been used before, but I've never seen them:

Variant 1: Musical chairs

Nonets 1 and 9 as well as nonets 3 and 7 share a special relationship.

If you had all of Nonet 1 solved, you could then copy it onto nonet 9. Then, you would have to move every number to a cell orthagonally or diagonally adjacent.

In other words, corresponding cells (R1C1 and R7C7, for example) cannot have the same value. The value of R1C1 must be in either R8C78 or R8C7.

Here's a visual example that might help:

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`N1 N9`

--- 11-

1-- -1-

--- 11-

Given the 1 in N1, the 1 in N9 can only be one of the 1's shown

N1 N9

--- ---

-22 ---

-2- --2

Given the 2 in N9, the 2 in N1 can only be one of the 2's shown

(The system works both ways)

N3 N7

--- 333

-3- 3-3

--- 333

Variant 2: Resonance Groups

In each of the 4 resonance groups-colored red, green, blue, yellow-there are exactly 3 pairs of like numbers and there are no more than 2 of any number. A resonance group of 7 for example could contain 2234477.

Variant 3: Differences

If any of these variants has been done before, it's probably this one.

The value in the grey circles is equal to the positive difference between the values of the numbers in the red circles connected to them. The value of the green circle is the positive difference between R3C3 and R7C7 which is also equal to the positive difference between R7C3 and R3C7. If the circles and lines are confusing, here's the information:

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`|R3C3-R7c7| = |R7C3-R3C7| = R5C5`

|R3C3-R7C3| = R5C1

|R3C7-R7C7| = R5C9

|R3C3-R3C7| = R1C4

|R7C3-R7C7| = R9C6

Variant 4: Wheels

The 5 wheels each contain 4 values. These numbers will go in the cells the values are in, but (most of) the wheels are not rotated to the right position. Right now, they're simply set with the lowest number at the top.

Here's a visual explanation:

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`Say you have this wheel`

1

3 5

6

The nonet the wheel is in could be any of the following

-1- -5- -6- -3-

3-5 1-6 5-3 6-1

-6- -3- -1- -5-

This was a delightful puzzle to make and I hope it will be fun to solve.

I have a walkthrough and solution on hand if you get stuck.

Enjoy!