Hidden faces
Introduction
I am investigating the number of hidden faces for different rows of cubes. When the cubes are placed on a table, you cannot touch them or move them however you may move the table around.
Examples
When a cube is placed on a table only 5 of the faces can be seen. So 1 face is hidden.
Figure 1 on the dotted paper shows this.
When five cubes are placed on a table only 17 faces can be seen. So 13 faces are hidden.
Figure 2 on the dotted paper shows this.
Part 1
I will tackle this problem by investigating different numbers of cubes. These cubes that I'll be using are 1 cube, 2 cubes, 3 cubes, 4 cubes and 5 cubes. These cubes are shown on the dotted paper. This method is sensible because using the number of cubes I'd be using could lead to finding a formula easily.
Number of cubes
Number of faces seen
Number of faces hidden
Total number of faces
5
6
2
8
4
2
3
1
7
8
4
4
0
24
5
7
3
30
Patterns
Patterns that I noticed was in the column 'Number of faces seen' that when a cube has 5 faces seen, 2 cubes has 8 faces seen. Three cubes have 11 faces seen, 4 cubes have 14 faces seen and 5 cubes has 17 faces seen. Between each cube is a gap of 3. This could help me with my finding of a formula. I also noticed that in the column 'Number of faces hidden' that when a cube has 1 face hidden, 2 cubes have 4 faces hidden. Three cubes have 7 faces hidden, 4 cubes have 10 faces hidden and 5 cubes has 13 cubes hidden. Between each cube is a gap of 3. This could help me with my finding of a formula. Finally I noticed in the column 'Total number of faces' that when a cube has a total of 6 faces, 2 cubes has a total of 12 faces. Three cubes have a total of 18 faces, 4 cubes have a total of 24 faces and 5 cubes have a total of 30 faces. Between each cube is a gap of 6. This could help me with my finding of a formula. These are all the patterns that I have noticed.
Introduction
I am investigating the number of hidden faces for different rows of cubes. When the cubes are placed on a table, you cannot touch them or move them however you may move the table around.
Examples
When a cube is placed on a table only 5 of the faces can be seen. So 1 face is hidden.
Figure 1 on the dotted paper shows this.
When five cubes are placed on a table only 17 faces can be seen. So 13 faces are hidden.
Figure 2 on the dotted paper shows this.
Part 1
I will tackle this problem by investigating different numbers of cubes. These cubes that I'll be using are 1 cube, 2 cubes, 3 cubes, 4 cubes and 5 cubes. These cubes are shown on the dotted paper. This method is sensible because using the number of cubes I'd be using could lead to finding a formula easily.
Number of cubes
Number of faces seen
Number of faces hidden
Total number of faces
5
6
2
8
4
2
3
1
7
8
4
4
0
24
5
7
3
30
Patterns
Patterns that I noticed was in the column 'Number of faces seen' that when a cube has 5 faces seen, 2 cubes has 8 faces seen. Three cubes have 11 faces seen, 4 cubes have 14 faces seen and 5 cubes has 17 faces seen. Between each cube is a gap of 3. This could help me with my finding of a formula. I also noticed that in the column 'Number of faces hidden' that when a cube has 1 face hidden, 2 cubes have 4 faces hidden. Three cubes have 7 faces hidden, 4 cubes have 10 faces hidden and 5 cubes has 13 cubes hidden. Between each cube is a gap of 3. This could help me with my finding of a formula. Finally I noticed in the column 'Total number of faces' that when a cube has a total of 6 faces, 2 cubes has a total of 12 faces. Three cubes have a total of 18 faces, 4 cubes have a total of 24 faces and 5 cubes have a total of 30 faces. Between each cube is a gap of 6. This could help me with my finding of a formula. These are all the patterns that I have noticed.
