You have three covered boxes of Burmese rubies before you. You know there are a total of 30 identical seven-carat rubies in the three boxes. You can ask for a certain number of rubies from each box. If you ask for more than there are, you get none from that box. Otherwise, you get what you asked for from that box. For now, suppose you must state your requests in advance for all three boxes and have no chance to change your mind; that is, with no feedback.
Warm-Up. Given no further constraints, how many rubies do you ask for from each box?
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