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

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

      Delete
  2. @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.

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Source:
Sent to me by Gaurav Sinha

Problem:
Siddhant writes a Maths test and correctly answers 5 out of 6 Arithmetic questions and 20 out of 28 Geometry questions. In total, Siddhant scores 25 out of 34. 

Vaibhav writes another Maths test and correctly answers 20 out of 25 Arithmetic questions and 6 out of 9 Geometry questions. in total, Vaibhav scores 26 out of 34.

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a) Vaibhav scores more than Siddhant
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