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You need two of each, one as the default appearance and one to enter the Knockout Group, and the one that serves as the mass object needs to be at the top (obvioulsy, since the others are behind it), in this case the black one; and all paths have a stroke and no fill.
You can use the following steps, making sure the black one is at the top:
1) For the black path, select and Ctrl/Cmd+C+F (hold Ctrl/Cmd and press C then F) to create a copy in front, then lock the copy in the Layers palette (with the Layer expanded); this is the selected path, so easy to find;
2) Select the unlocked original from 1), then switch from stroke to fill, then set the Opacity to 0 in the Transparency palette;
3) For the other paths (red and blue and whichever additional paths you wish), select and Ctrl/Cmd+C+B (hold Ctrl/Cmd and press C then B) to create a copy in back, then lock the copy in the Layers palette (with the Layer expanded); this is the selected path, so easy to find;
3) For each of the other paths, ClickDrag over it with the Direct Selection Tool and apply Dashed Line as desired (you can hide the locked duplicate to see);
4) Select all the non selected paths and Ctrl/Cmd to form the Group, then tick Knockout Group in the Transparency palette enough times until you have a full tick mark;
5) Unlock all locked paths in the Layers palette; now you are ready to move;
To move any of the path sets round freely:
6) With the Direct Selection Tool, Alt/OptionClickDrag (hold Alt/Option and ClickDrag) over the path set(s) you wish to move to select it, making sure to avoid selecting other path sets that need to stay in place, then ClickDrag the path set(s) by any segment/Anchor Point to move to the desired position.
In 6), you can select multiple path sets (such as the red and blue one, avoiding the black one), so they are moved in the same way.
If you are unable to select all path sets you wish to move in the same way at the same time in 6), you can use ShiftAlt/OptionClickDrag (hold both Shift and Alt/Option and ClickDrag) to select the path sets in multiple steps.
The Alt/Option lets you select whole paths.
The Shift lets you select more path sets together; you can skip it for the first set, but it is simpler and safer to use it throughout.
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