The sheet shows this as an example. It is a line of five cubes and it has 30 faces and 13 of the faces are hidden.
I tried changing the amount of cubes, to see what results I Got.
I used 7 cubes and noticed that I now had 42 faces and 19 of the faces are hidden.
I used 6 cubes and noticed that I now had 36 faces and 16 of the faces are hidden.
I used 1 cube and noticed that I now had 6 faces and 1 of the faces are hidden.
I used 10 cubes and noticed that I now had 6 faces and 28 of the faces are hidden.
I then compiled a table with all the information about the cubes which provided details of the: amount of cubes, hidden faces, number of sides and seen faces. Look at the table below to see.
The table is showing here that when a cube is added the number of sides goes up by 6, the seen faces go up by 3 and then hidden faces goes up by 3. This pattern now helped me predict the next two cubes 6 and 7. To see my predictions look below.
Soon after the predictions I made I thought I could come up with a simple rule which will help me calculate the amount of hidden faces without getting cubes out and counting them.
For each cube 6 sides were added on.
E.G. 1 cube = 6 sides
2 cubes = 12 sides
To work out the number of seen faces you would do this = cube x 3 + 2
E.G. 3 cubes x 3 + 2 = 11
4 cubes x 3 + 2 = 14
As you can see there is a pattern emerging of + 3
Working out the number of seen faces was a big step to helping me solve a rule to work out the amount of hidden faces. For every seen face/s if you took away 4 from it you would get the amount of hidden faces for that cube.
E.G. 5 cubes = 17 seen faces – 4 = 13 hidden faces
6 cubes = 20 seen faces – 4 = 16 hidden faces
There is a pattern emerging of – 3
Soon after all these predictions I then went on to write out my rule. The rule that I came out with was:
This rule was consistent and worked as you can see :
1 cube x 3 = 3 – 2 = 1
2 cubes x 3 = 6 – 2 = 4
3 cubes x 3 = 9 – 2 = 7
Here was part of the table made which I collected the results which I counted myself using 3D cubes.
As you can see the results came up correct. That’s the end of investigation 1
Part 2