Minimum moveset array

[CronusNuzlocker]

This may be something everyone's looked at before. But I didn't know and couldn't find the list online so I decided to work it out myself.
Obviously, since there are type combinations that change a pokemon's weakness and resistance to a particular type, there must be a minimum set of types needed to provide super effective coverage across every type combination.
Due to it's ability Levitate, Eelektross is the only pokemon not covered by this list as it doesn't have a weakness

I started by making a list of every existent type combination and their relationship to each type(excel lookup tables automated the process)
Second I selected the type with the most combinations that are 4x weak to it. This type in case you're wondering is ICE.
With the type selected I removed every combination with a 2x or 4x weakness to it and continued on repeating the process.

I understand this is likely not the ONLY list, but it is the smallest one I found. The following 9 types provide a super effective move against every current(Except Eelektross) pokemon as of ORAS:

Ice, Ground, Rock, Fire, Fairy, Grass, Poison, Dark, Fighting.(Fighting is only needed for pure Normal type pokemon. With their exception the other 8 cover everything)
What do you think? Is there a smaller list? Is this list at all important?

 

[skyradiant]

It's not really that important to hit everything for super-effective damage, since strong STAB-moves will often do the job just fine (unresisted of course).

 

[CronusNuzlocker]

It's not really that important to hit everything for super-effective damage, since strong STAB-moves will often do the job just fine (unresisted of course).

I know, STAB can make all the difference. I was just curious what the minimum set of super-effective types are for all pokemon.

 

[firepanda]

Well at a bare minimum you need Ground (for electric types), Fighting (for normal types), Ground (for Drapion), Grass (for Whiscash) and Fire (for Scizor). That alone hits most pokemon super effectively.

After that you start to lose your determinism. (Incidentally, I think this is a better way of thinking about the problem. It's still greedy, but you'll cover the tricky cases first by looking at the obscure types, rather than going in 'type-first' which just uses up types.) But we have five types at the moment and you've shown that 9 is an upper bound on our optimal solution. So we're only allowed three types to find something better.

For instance, Fairies aren't hit super effectively, so we need either Steel or Poison in that list. Likewise for Flying (Electric, Ice or Rock) and Ghosts (Dark or Ghost). Since all these se types are different (and pure Flying, Fairy and Psychic types exist), we need at least one from each list to hit everything super-effectively. That brings us to 8, which is the most we're allowed, otherwise we're no better than your solution. So there are only 2 * 2 * 3 = 12 combinations to find something better than yours.

I'll let you do the rest. I think your solution up there is optimal.