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Collections are a way for you to organize kata so that you can create your own training routines. Every collection you create is public and automatically sharable with other warriors. After you have added a few kata to a collection you and others can train on the kata contained within the collection.
Get started now by creating a new collection.
7 teams will start tournament directly from part 2 (7 is odd number, part 1 will be skipped), were they must play each with other, thus 21 games will be played instead of 7, meanwhile 8 teams will 4 quadfinals, play 2 semifinals, 1 final = 7 games, just much as you need. So, here only one correct answer: 8 teams.
Second case is the same, 67108863 teams will play 2_251_799_713_021_953 games, instead of 67108863.