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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.
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(disregard the previous reply if it appears on your end, it has disappeared for me)
The code in my original kumite fork returns true for the test you mention. It must be something to do with the changes made to resolve the repeating names thing.
Regarding turning this into a kata, my thought is that inputs should be guaranteed valid (eg no item in the rules refers to a nonexistent family, no repeating members in the list, no member wants to sit next to themself, etc)
Do you have a link to your updated set of tests? That would be helpful.