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Cutting corners. (Posted on 2014-08-14) Difficulty: 3 of 5

I cut off one corner of an empty box to form an open 'pocket', so that each of the length a, breadth b, and depth c, of the initial corner was a different whole number of centimetres, and the area of each face of the 'pocket' was also an integer.

What is the area of the open 4th side of the 'pocket', in terms of a,b, and c?

See The Solution Submitted by broll    
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Some Thoughts re: what is wanted? | Comment 2 of 5 |
(In reply to what is wanted? by Charlie)

I noted some instances where the a, b and c were not all distinct. I've now also counted only those instances where the 4th side also has integer area:


  1  2  8      9.0000000000   11
  2  4  6     14.0000000000   12
  2  6  8     26.0000000000   16
  2  8 10     42.0000000000   20
  4  6 10     38.0000000000   20
  2  3 16     29.0000000000   21
  2  4 16     36.0000000000   22
  6  8  9     51.0000000000   23
  2 10 12     62.0000000000   24
  4  8 12     56.0000000000   24
  3  8 14     61.0000000000   25
  4  7 16     66.0000000000   27
  5  8 14     69.0000000000   27
  2 12 14     86.0000000000   28
  4  6 18     66.0000000000   28
  4 10 14     78.0000000000   28
  6  8 14     74.0000000000   28
  8 10 11     81.0000000000   29
  2 14 16    114.0000000000   32
  4 12 16    104.0000000000   32
  6 10 16     98.0000000000   32
  3  6 24     81.0000000000   33
  2  9 24    111.0000000000   35
  6 13 16    121.0000000000   35
  2 16 18    146.0000000000   36
  4 14 18    134.0000000000   36
  6 12 18    126.0000000000   36
  8 10 18    122.0000000000   36
  1  4 32     66.0000000000   37
  1  8 30    121.0000000000   39
 11 12 16    146.0000000000   39
  2 18 20    182.0000000000   40
  4 16 20    168.0000000000   40
  6 14 20    158.0000000000   40
  8 12 20    152.0000000000   40
  7  8 26    141.0000000000   41
  4  6 32    116.0000000000   42
  8 10 25    165.0000000000   43
  2  6 36    114.0000000000   44
  2 20 22    222.0000000000   44
  4  8 32    144.0000000000   44
  4 18 22    206.0000000000   44

  Posted by Charlie on 2014-08-14 16:41:17
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