DAY 79

Comment

The framework consists of a cube at each of 8 corners, joined by 12 identical lines of cubes.
So you need to know the length of each line of cubes for the 12 cm framework.

Answer

128 cubes are needed for the 12 cm cube framework.

Readers' methods

Lorna Hislop, Leominster HR6:
The base is made of 44 cubes (12 + 10 + 12 + 10).
The top is also made of 44 cubes.
The base and top are joined by 4 columns of 10 cubes, which is 40 cubes.
44 + 44 + 40 = 128.

Martin F, Manchester M21:
Each framework is made up of 4 sides at the full length of the side
plus 8 sides at 2 less than the full length.
So the 12 cm cube framework will have 4 @ 12 cubes + 8 @ 10 cubes
which is 128 cubes.

Francesca W, LondonWC1X:
Every cube contains 12 sides and 8 corners.
Each side contains 2 corner cubes.
General method:
Total number of cubes = 12 x (y - 2) + 8,
where y is the length of the sides of the cube in cm.
So a 12 cm cube framework has 12 x (12 - 2) + 8 = 128 cubes.

Bernd F, Aulendorf, Germany:
First I calculated how many small cubes there are in the big solid cube:12x12x12=1728.
To get the framework, you have to take off an inner cube 10x10x10=1000 (728 1cm cubes remaining) and six times the quadrilateral (the hole) in the faces of the big solid cube.
So I subtracted another 600 and got 128 1cm cubes as the solution.

RM, UK:
The given framework has 56 cubes.
The new framework will need 6 extra cubes on each of the 12 edges = 72 extra cubes.
56 + 72 = 128.