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Can it be done? A team example would be helpful. And the movesets.

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No, because 17 is not divisible by 6. There would be 5 types leftover.

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but what if each pokemon knows a diff type of move?
well, how do you mean? by covering every type with a given move in the team?
Each pokemon can have 4 moves, and with six pokemon that's 24 moveslots. So yes, you could a move of every of the seventeen types on a team, with seven spare moveslots.
thanks brotad thats what i meant. :)
Taking the worst case scenario that you need 17 moves to cover each type: each Pokemon can learn 4 moves, therefore a maximum of 24 moves are available in a team of 6. So yes, you can cover every type super-effectively in a team of 6.
It should be noted that all types can be hit supereffectively with just six types: ground, fighting, dark/ghost, grass, ice and flying, not taking dual types into account
thanks brotad and fondant for answering my qustion
Speaking to Grievous

I don't know if you know this your not but i'm assuming you don't. Not every type covers the exact same number of types in terms of super effectiveness. even if they did and they all covered exactly 3 different types and all types we're covered by at least 1 type it would be possible because 6x3=18 which is more than 17.

HOWEVER. not all types cover the same number of types, some types are only super effective against 2 types and some against 5. so if you look closely you can find a combination of 6 that covers 17. in fact there are about 4 combinations of 6 that cover 17.

Please do some basic math the next time someone asks a math related question. It annoys me when people answer good questions with answers that don't make sense.
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well...actually you can

i dont know about a team, I will leave that to you but:

Electric(covers Flying and Water)
Ice(covers Ground, Flying, Dragon and Grass)
Fight(covers Normal, Dark, Rock, Steel and Ice)
Ground(covers Electric, Steel, Poison, Fire and Rock)
Flying(covers Fighting, Bug and Grass, not affected by Ground)
Dark(covers Psychic and Ghost) you can build your team based of these types

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