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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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Maybe they could test something 100 times smaller with (linearly? quadratically?) proportionally less time for us test using 'Run tests', so that we have the benefit of not having to load 20MB of numbers.
"My below solution is to leave the "state" of the locker unchanged if the number of locker is a multiple of the run." I would say it's the other way around, i.e. on the 7th run he only alters the state of all multiples of 7. But I agree that kata description is a bit confusing.