Hanging a picture frame

The following problems appeared in The Riddler. It’s a problem about knots! Or rather, not-knots.

Imagine a framed picture suspended by a cord that’s hanging on two nails. If the picture were hung “normally,” you’d expect the removal of one nail to leave the picture hanging from the other (albeit a bit askew). But how can you hang a picture on two nails so that if you remove either nail the picture will crash to the floor?

What about three nails? What about four nails? What about on two red nails and two blue nails such that the picture falls if both red nails are removed and if both blue nails are removed but remains hanging if one of each color is removed?

Here is my solution for the case of two nails:
[Show Solution]

Here is my solution for the cases of three and four nails:
[Show Solution]

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