Giza-IQ Test - Solution 7

The cubic root of 2 is 1.259921049894873 = ~1.26

The following table shows how many 2-cubes (i.e., cubes of volume 2) fit side-by-side into the length occupied by a given number of 1-cubes:

1-cubes 2-cubes

   1      0

   2      1   1.26

   3      2   2.52

   4      3   3.78

   5      3   3.78

   6      4   5.04

   7      5   6.30

   8      6   7.56

   9      7   8.82

  10      7   8.82

  11      8  10.08

For example, six 2-cubes need just a bit less space than eight 1-cubes.

To solve the problem, we only need try possible box dimensions starting from the smallest one that can contain a 2-cube. We can afford to do so, because we expect to find a solution pretty soon.

1-cubes   1-vol   2-cubes   2-vol   ratio

2x2x2       8     1x1x1       2      1/4

2x2x3      12     1x1x2       4      1/3

2x3x3      18     1x2x2       8      4/9

3x3x3      27     2x2x2      16     16/27

2x2x4      16     1x1x3       6      3/8

2x3x4      24     1x2x3      12      1/2

3x3x4      36     2x2x3      24      2/3

3x4x4      48     2x3x3      36      3/4

4x4x4      64     3x3x3      54     27/32

2x2x5      20     1x1x3       6      3/10

2x3x5      30     1x2x3      12      2/5   ***