### Hanging Picture Puzzle

**Source:**Mailed to me by Sudeep Kamath (PhD Candidate UC Berkeley, EE IITB 2008 Alumnus)

**Problem:**

Suppose we have a portrait hung on a wall using one nail. Now, suppose we hammer another nail next to the existing one and try to use both nails to hang the portrait. If any nail breaks, the portrait continues to hang safely. Can we hang the portrait in such a way that if any one nail breaks the portrait must fall down?

Generalize to

*k*nails: Hang a portrait on

*k*nails such that if any one nail breaks, the portrait must fall down.

Cheeky little back-of-the-envelope sketch.

ReplyDeleteWhat if all the nails are vertically aligned and you hang the picture on the lowest nail.

ReplyDeleteIt says if any nail breaks, the portrait should fall down which doesn't happen in your case right.

Delete@Jim,

ReplyDeleteYou assume that the picture is actually just literally hanging on a string. I believe the standard hanging picture puzzle assumes that the picture has two points where strings are fixed, much like tied on nails on the picture. With that assumption, your solution will not work.

But given your assumption, I think your solution is great and amazing.

Thanks a ton.

Fair enough, Pratik. Easily remedied :)

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