Quickly generating possible numerical distributions (sequencing with repeating variables)

bcc.phillips.97

I don't have trouble with generating possible numerical distributions for In/Out or Grouping games, but for some reason I struggle to be able to quickly write out all the possible distributions for linear sequencing games with repeating variables (i.e. June 2007 Game 3). Is there a quick and easy trick to doing this? I find it involves a lot of overthinking and is a slow process for me.

5Fennel LSAT

Recently revisited this so here is one strategy to answer your question: Even though it's a sequence, not fundamentally different to what you might do for an in/out grouping game.

7 spots, 4 items. Every week will be a visit (no blanks). Each destination will be in (none out). From this infer some will repeat.

Given must be in: GJMMT.

5/7 items are established, 2 spots are indeterminate. M is fixed at 2, so the only three possible repeaters are G, J, and T.

From there you can infer the limited set of combinations for the final two spots, subject to the other rules may further limit the possible combinations and permutations (just going to leave it here to answer your original question).

Broad applicable strategy: Determine elements that must be in, count remaining indeterminate spots and evaluate combinations of the possible remaining repeating pieces.