I want to make a game where there's a total of 10 general weapon types. I want any given character to be able to be proficient with 2 of the weapon types. Looking at the fact that 10 is an even number, a perfect rock-paper-scissors relationship wouldn't be possible. "C(10,2)=45" however is an odd number, which should be workable into a rock-paper-scissors system.
Since the final number of total weapon pairings is an odd number, I reckon there should be an intuitive and systemically organized way to get a rock-paper-scissors relationship to exist where each weapon pairing is at an advantage against 22 of the other pairings while being at a disadvantage against the remaining 22 pairings. Assuming the 10 weapon types that a character can be proficient with 2 of are labeled A through to J, how should I organize it?
P.S.: A smaller example that runs into the same situation would be "C(6,2)=15"; weapons labeled A through F; if that's more convenient for explanation purposes. Please let me know if this question belongs under different tags or even over on the Mathematics section of SE instead of here; I wasn't sure where to put this question.