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.


Comments

  1. JDGM7:47 PM, December 05, 2012

    Cheeky little back-of-the-envelope sketch.

    ReplyDelete
  2. Anonymous2:45 AM, December 13, 2012

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

    ReplyDelete
    Replies
    1. INNER VOICE11:16 PM, December 19, 2012

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

      Delete
  3. Pratik Poddar12:24 AM, December 26, 2012

    @Jim,

    You 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.

    ReplyDelete
  4. JDGM11:35 AM, December 31, 2012

    Fair enough, Pratik. Easily remedied :)

    ReplyDelete
  5. Vivek 7:42 PM, April 19, 2013

    This comment has been removed by the author.

    ReplyDelete
  6. Vivek 4:57 AM, April 20, 2013

    This comment has been removed by the author.

    ReplyDelete

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