Homework SourseI need to write in an Excel file all the possible combinatio
I need to write in an Excel file all the possible combinations of 4 numbers in sets of 4 including the repeated numbers. For example, if the numbers were 0 1 2 3, then 0 0 0 0, 1 1 1 1 & all possible combinations & all orders like 0 1 2 3, 3 2 1 1, 2 2 3 3 , 3 0 1 3, etc. Pls advise.
Solution
The key to enumerating is this:
Fill in the first column with 64 0s, 64 1s, 64 2s, 64 3s.
Fill in the second column with 16 0\'s, 16 1\'s, 16 2\'s, 16 3\'s, alternatingly.
Fill in the third column with 4 0\'s, 4 1\'s, 4 2\'s, 4 3\'s, alternatingly.
Fill in the fourth column with 0\'s, 1\'s, 2\'s, 3\'s, alternatingly.
This is the result:
| 0 | 0 | 0 | 0 |
| 0 | 0 | 0 | 1 |
| 0 | 0 | 0 | 2 |
| 0 | 0 | 0 | 3 |
| 0 | 0 | 1 | 0 |
| 0 | 0 | 1 | 1 |
| 0 | 0 | 1 | 2 |
| 0 | 0 | 1 | 3 |
| 0 | 0 | 2 | 0 |
| 0 | 0 | 2 | 1 |
| 0 | 0 | 2 | 2 |
| 0 | 0 | 2 | 3 |
| 0 | 0 | 3 | 0 |
| 0 | 0 | 3 | 1 |
| 0 | 0 | 3 | 2 |
| 0 | 0 | 3 | 3 |
| 0 | 1 | 0 | 0 |
| 0 | 1 | 0 | 1 |
| 0 | 1 | 0 | 2 |
| 0 | 1 | 0 | 3 |
| 0 | 1 | 1 | 0 |
| 0 | 1 | 1 | 1 |
| 0 | 1 | 1 | 2 |
| 0 | 1 | 1 | 3 |
| 0 | 1 | 2 | 0 |
| 0 | 1 | 2 | 1 |
| 0 | 1 | 2 | 2 |
| 0 | 1 | 2 | 3 |
| 0 | 1 | 3 | 0 |
| 0 | 1 | 3 | 1 |
| 0 | 1 | 3 | 2 |
| 0 | 1 | 3 | 3 |
| 0 | 2 | 0 | 0 |
| 0 | 2 | 0 | 1 |
| 0 | 2 | 0 | 2 |
| 0 | 2 | 0 | 3 |
| 0 | 2 | 1 | 0 |
| 0 | 2 | 1 | 1 |
| 0 | 2 | 1 | 2 |
| 0 | 2 | 1 | 3 |
| 0 | 2 | 2 | 0 |
| 0 | 2 | 2 | 1 |
| 0 | 2 | 2 | 2 |
| 0 | 2 | 2 | 3 |
| 0 | 2 | 3 | 0 |
| 0 | 2 | 3 | 1 |
| 0 | 2 | 3 | 2 |
| 0 | 2 | 3 | 3 |
| 0 | 3 | 0 | 0 |
| 0 | 3 | 0 | 1 |
| 0 | 3 | 0 | 2 |
| 0 | 3 | 0 | 3 |
| 0 | 3 | 1 | 0 |
| 0 | 3 | 1 | 1 |
| 0 | 3 | 1 | 2 |
| 0 | 3 | 1 | 3 |
| 0 | 3 | 2 | 0 |
| 0 | 3 | 2 | 1 |
| 0 | 3 | 2 | 2 |
| 0 | 3 | 2 | 3 |
| 0 | 3 | 3 | 0 |
| 0 | 3 | 3 | 1 |
| 0 | 3 | 3 | 2 |
| 0 | 3 | 3 | 3 |
| 1 | 0 | 0 | 0 |
| 1 | 0 | 0 | 1 |
| 1 | 0 | 0 | 2 |
| 1 | 0 | 0 | 3 |
| 1 | 0 | 1 | 0 |
| 1 | 0 | 1 | 1 |
| 1 | 0 | 1 | 2 |
| 1 | 0 | 1 | 3 |
| 1 | 0 | 2 | 0 |
| 1 | 0 | 2 | 1 |
| 1 | 0 | 2 | 2 |
| 1 | 0 | 2 | 3 |
| 1 | 0 | 3 | 0 |
| 1 | 0 | 3 | 1 |
| 1 | 0 | 3 | 2 |
| 1 | 0 | 3 | 3 |
| 1 | 1 | 0 | 0 |
| 1 | 1 | 0 | 1 |
| 1 | 1 | 0 | 2 |
| 1 | 1 | 0 | 3 |
| 1 | 1 | 1 | 0 |
| 1 | 1 | 1 | 1 |
| 1 | 1 | 1 | 2 |
| 1 | 1 | 1 | 3 |
| 1 | 1 | 2 | 0 |
| 1 | 1 | 2 | 1 |
| 1 | 1 | 2 | 2 |
| 1 | 1 | 2 | 3 |
| 1 | 1 | 3 | 0 |
| 1 | 1 | 3 | 1 |
| 1 | 1 | 3 | 2 |
| 1 | 1 | 3 | 3 |
| 1 | 2 | 0 | 0 |
| 1 | 2 | 0 | 1 |
| 1 | 2 | 0 | 2 |
| 1 | 2 | 0 | 3 |
| 1 | 2 | 1 | 0 |
| 1 | 2 | 1 | 1 |
| 1 | 2 | 1 | 2 |
| 1 | 2 | 1 | 3 |
| 1 | 2 | 2 | 0 |
| 1 | 2 | 2 | 1 |
| 1 | 2 | 2 | 2 |
| 1 | 2 | 2 | 3 |
| 1 | 2 | 3 | 0 |
| 1 | 2 | 3 | 1 |
| 1 | 2 | 3 | 2 |
| 1 | 2 | 3 | 3 |
| 1 | 3 | 0 | 0 |
| 1 | 3 | 0 | 1 |
| 1 | 3 | 0 | 2 |
| 1 | 3 | 0 | 3 |
| 1 | 3 | 1 | 0 |
| 1 | 3 | 1 | 1 |
| 1 | 3 | 1 | 2 |
| 1 | 3 | 1 | 3 |
| 1 | 3 | 2 | 0 |
| 1 | 3 | 2 | 1 |
| 1 | 3 | 2 | 2 |
| 1 | 3 | 2 | 3 |
| 1 | 3 | 3 | 0 |
| 1 | 3 | 3 | 1 |
| 1 | 3 | 3 | 2 |
| 1 | 3 | 3 | 3 |
| 2 | 0 | 0 | 0 |
| 2 | 0 | 0 | 1 |
| 2 | 0 | 0 | 2 |
| 2 | 0 | 0 | 3 |
| 2 | 0 | 1 | 0 |
| 2 | 0 | 1 | 1 |
| 2 | 0 | 1 | 2 |
| 2 | 0 | 1 | 3 |
| 2 | 0 | 2 | 0 |
| 2 | 0 | 2 | 1 |
| 2 | 0 | 2 | 2 |
| 2 | 0 | 2 | 3 |
| 2 | 0 | 3 | 0 |
| 2 | 0 | 3 | 1 |
| 2 | 0 | 3 | 2 |
| 2 | 0 | 3 | 3 |
| 2 | 1 | 0 | 0 |
| 2 | 1 | 0 | 1 |
| 2 | 1 | 0 | 2 |
| 2 | 1 | 0 | 3 |
| 2 | 1 | 1 | 0 |
| 2 | 1 | 1 | 1 |
| 2 | 1 | 1 | 2 |
| 2 | 1 | 1 | 3 |
| 2 | 1 | 2 | 0 |
| 2 | 1 | 2 | 1 |
| 2 | 1 | 2 | 2 |
| 2 | 1 | 2 | 3 |
| 2 | 1 | 3 | 0 |
| 2 | 1 | 3 | 1 |
| 2 | 1 | 3 | 2 |
| 2 | 1 | 3 | 3 |
| 2 | 2 | 0 | 0 |
| 2 | 2 | 0 | 1 |
| 2 | 2 | 0 | 2 |
| 2 | 2 | 0 | 3 |
| 2 | 2 | 1 | 0 |
| 2 | 2 | 1 | 1 |
| 2 | 2 | 1 | 2 |
| 2 | 2 | 1 | 3 |
| 2 | 2 | 2 | 0 |
| 2 | 2 | 2 | 1 |
| 2 | 2 | 2 | 2 |
| 2 | 2 | 2 | 3 |
| 2 | 2 | 3 | 0 |
| 2 | 2 | 3 | 1 |
| 2 | 2 | 3 | 2 |
| 2 | 2 | 3 | 3 |
| 2 | 3 | 0 | 0 |
| 2 | 3 | 0 | 1 |
| 2 | 3 | 0 | 2 |
| 2 | 3 | 0 | 3 |
| 2 | 3 | 1 | 0 |
| 2 | 3 | 1 | 1 |
| 2 | 3 | 1 | 2 |
| 2 | 3 | 1 | 3 |
| 2 | 3 | 2 | 0 |
| 2 | 3 | 2 | 1 |
| 2 | 3 | 2 | 2 |
| 2 | 3 | 2 | 3 |
| 2 | 3 | 3 | 0 |
| 2 | 3 | 3 | 1 |
| 2 | 3 | 3 | 2 |
| 2 | 3 | 3 | 3 |
| 3 | 0 | 0 | 0 |
| 3 | 0 | 0 | 1 |
| 3 | 0 | 0 | 2 |
| 3 | 0 | 0 | 3 |
| 3 | 0 | 1 | 0 |
| 3 | 0 | 1 | 1 |
| 3 | 0 | 1 | 2 |
| 3 | 0 | 1 | 3 |
| 3 | 0 | 2 | 0 |
| 3 | 0 | 2 | 1 |
| 3 | 0 | 2 | 2 |
| 3 | 0 | 2 | 3 |
| 3 | 0 | 3 | 0 |
| 3 | 0 | 3 | 1 |
| 3 | 0 | 3 | 2 |
| 3 | 0 | 3 | 3 |
| 3 | 1 | 0 | 0 |
| 3 | 1 | 0 | 1 |
| 3 | 1 | 0 | 2 |
| 3 | 1 | 0 | 3 |
| 3 | 1 | 1 | 0 |
| 3 | 1 | 1 | 1 |
| 3 | 1 | 1 | 2 |
| 3 | 1 | 1 | 3 |
| 3 | 1 | 2 | 0 |
| 3 | 1 | 2 | 1 |
| 3 | 1 | 2 | 2 |
| 3 | 1 | 2 | 3 |
| 3 | 1 | 3 | 0 |
| 3 | 1 | 3 | 1 |
| 3 | 1 | 3 | 2 |
| 3 | 1 | 3 | 3 |
| 3 | 2 | 0 | 0 |
| 3 | 2 | 0 | 1 |
| 3 | 2 | 0 | 2 |
| 3 | 2 | 0 | 3 |
| 3 | 2 | 1 | 0 |
| 3 | 2 | 1 | 1 |
| 3 | 2 | 1 | 2 |
| 3 | 2 | 1 | 3 |
| 3 | 2 | 2 | 0 |
| 3 | 2 | 2 | 1 |
| 3 | 2 | 2 | 2 |
| 3 | 2 | 2 | 3 |
| 3 | 2 | 3 | 0 |
| 3 | 2 | 3 | 1 |
| 3 | 2 | 3 | 2 |
| 3 | 2 | 3 | 3 |
| 3 | 3 | 0 | 0 |
| 3 | 3 | 0 | 1 |
| 3 | 3 | 0 | 2 |
| 3 | 3 | 0 | 3 |
| 3 | 3 | 1 | 0 |
| 3 | 3 | 1 | 1 |
| 3 | 3 | 1 | 2 |
| 3 | 3 | 1 | 3 |
| 3 | 3 | 2 | 0 |
| 3 | 3 | 2 | 1 |
| 3 | 3 | 2 | 2 |
| 3 | 3 | 2 | 3 |
| 3 | 3 | 3 | 0 |
| 3 | 3 | 3 | 1 |
| 3 | 3 | 3 | 2 |
| 3 | 3 | 3 | 3 |
