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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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I think they divided by 2 because the smallest divisor you can have is 2 or above meaning all numbers will be less than x/2 and flooring it was because divisors are only full numbers. The question mark is an if statement. First you have your statement then the question mark then the code to be ran if true and the colon is an else followed by the code for the else