Suppose I have 3 letters a, b, c and I want to find the minimum length of a string that uses all the double combinations of the aforementioned letters.
How should I do it or how are such problems called in order to search for them online?
Example:
The 3 letters a, b, c produce 9 double combinations:
- aa
- bb
- cc
- ab
- ac
- bc
- ba
- ca
- cb
What I want is a string that in its length will include all the combinations only one time or a minimum number of times, which in this case is only one time. For example the aabbcc includes the combinations: 1, 2, 3, 4, 6 like this:
- 1: aa bbcc
- 2: aa bb cc
- 3: aabb cc
- 4: a ab bcc
- 6: aab bc c
The string that I want is actually this:
aabbccacba which includes all the double combinations only once:
- 1: aa bbccacba
- 2: aa bb ccacba
- 3: aabb cc acba
- 4: a ab bccacba
- 6: aab bc cacba
- 8: aabbc ca cba
- 5: aabbcc ac ba
- 7: aabbccac ba
- 9: aabbcca cb a
I am not concerned about the order that the combinations appear, so any similar string that includes the 9 combinations a minimum number of times would suffice. I only need that the double combinations to appear the minimum number of times.
The above concerns 3 letters and double combinations; let's call it a 3:2 problem. Imagine now that I want to have the flexibility to produce this string for 4:3, 7:2, 9:6 problems, etc...
Sincere apologies if this is not a question on mathematics.