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ValeryOchkov24-Ruby IV
24-Ruby IV
February 22, 2013
Question

The problem with boxes - 1, 5, 21...

  • February 22, 2013
  • 11 replies
  • 5746 views

We cut out from one square sheet (cardboard), four small squares and make a cross-shaped piece out of the box. Then we cut out of four small square sheets sixteen more small squares and make them into new boxes and so on to infinity. What will be the maximum amount of an infinite number of boxes?http://twt.mpei.ac.ru/ochkov/Mathcad_12/3_09_5_Box.png

11 replies

ValeryOchkov24-Ruby IVAuthor
24-Ruby IV
February 22, 2013

One solution for a one box:

http://twt.mpei.ac.ru/ochkov/Mathcad_12/3_08_Box.png

AlanStevens19-Tanzanite
19-Tanzanite
February 26, 2013

I think the total volume is given by V=a(1-2a)^2/(1-4a^3), where the value of 'a' to give maximum volume is 0.174 and the corresponding value of V is 0.076.

See attached.

Alan

ValeryOchkov24-Ruby IVAuthor
24-Ruby IV
February 26, 2013

Thanks, Alan!

What can you say about this solution:

http://twt.mpei.ac.ru/ochkov/Mathcad_12/3_10_N_Box.png

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