Sounds like you have two circuits running into each other someplace - either by switchlegs as described by a member, or a makeup mistake in a J-Box.
If the system is 3 phase, that puts Ckt. 6 on phase C and Ckt 31 on phase A.
One other place to find the fault location would be inside light fixtures where bilevel or "a/b" switching is used.
Have found this to be the most common makeup mistake when breakers trip as you have described.
Finding the person that did the makeup is difficult on large jobs [so you can explain the mistake and why it needs to be avoided, not to do any finger pointing or put downs]. Typically it's a Helper that is under pressure, or a Journeyman having a bad day.
From your description it sure sounds like the two circuits got tied together someplace by mistake. If I am correct, you could leave one of the breakers off, turn the other on and nothing pops. You will also read voltage at the load terminal of the breaker that's in the off position.
The real problem lies in finding where the mistake is at without opening too many things. Correcting it is simple.
If the system is 277/480 and the main service is 1000 amps or higher, you would know if this was a ground fault. The main would trip! [GFPE type main].
Let us know of the outcome.