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Cardboard Conclusion (Posted on 2014-06-08) Difficulty: 3 of 5
Determine the total number of 3 x 5 rectangular pieces of cardboard that can be cut from a 17 x 22 rectangular piece of cardboard such that the amount of waste is a minimum.

No Solution Yet Submitted by K Sengupta    
Rating: 3.0000 (1 votes)

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Solution Minimizing the waste (spoiler) | Comment 1 of 3
17 * 22 = 374, so the theoretical maximum is 24 pieces (360 unit area), with 14 unit area left over.  This is in fact achievable.  One way:

a) Orient the card board so that it is 17 high and 22 wide.
b) From the NorthWest corner, cut a piece that is 6 high and 10 wide.  Divide into 4 pieces.
c) From the SouthWest corner, cut a piece that it 10 high and 12 wide.  Divide into 8 pieces.
d) From the SouthEast corner, cut a piece that is 12 high by 10 wide.  Divide into 8 pieces.
e) From the NorthEast corner, cut a piece that is 5 high by 12 wide.  Divide into 4 pieces.

This gives 24 pieces, plus one continuous piece with 14 unit squares.

Edited on June 8, 2014, 11:36 am
  Posted by Steve Herman on 2014-06-08 11:35:30

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