Scalability Matrix
for the game of Tic-Tac-Toe
| Dim |
Recom-
mended
Players |
Matrix |
1st-Move |
1st-Round of Moves |
Winning Moves |
| Possibilities |
Generic |
Possibilities |
Unique |
Possible |
Generic |
| n |
n |
(n+1)n |
(n+1)n |
- |
- |
- |
- |
- |
| 2 |
2 |
3 x 3 |
3 * 3
= 9 |
3 |
9 * 8
= 72 |
12 |
8 |
3 |
| 3 |
3 |
4 x 4 x 4 |
4 * 4 * 4
= 64 |
3 |
64 * 63 * 62
= 249,984 |
? |
72 |
3 |
| 4 |
4 |
5 x 5 x 5 x 5 |
5 * 5 * 5 * 5
= 625 |
6 |
625 * 624 * 623 * 622
= 151,127,340,000 |
? |
? |
4 |
| 5 |
5 |
6 x 6 x 6 x 6 x 6 |
6 * 6 * 6 * 6 * 6
= 7,776 |
6 |
7776 * 7775 * 7774 * 7773 * 7772
= 28,393,742,898,980,409,600 |
? |
? |
4 |
| 6 |
6 |
7 x 7 x 7 x 7 x 7 x 7 |
7 * 7 * 7 * 7 * 7 * 7
= 823,543 |
10 |
823543 * 823542 * 823541 *
823540 * 823539 * 823538
= a very big number |
? |
? |
5 |
| 7 |
7 |
8 x 8 x 8 x 8 x 8 x 8 x 8 |
8 * 8 * 8 * 8 * 8 * 8 * 8
= 2,097,152 |
10 |
2097152 * 2097151 * 2097150 *
2097149 * 2097148 * 2097147 *
2097146
= a very, very big number |
? |
? |
5 |
| ... |
... |
... |
... |
... |
... |
... |
... |
... |
|
| If this is the scalability matrix of a simple children's game (Tic-Tac-Toe), then just imagine what the scalability matrix looks like for a large mutli-national corporation! |
