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You have n numbers that must sum to 10. So your first number plus your second
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number, plus all the way to the nth number, has to equal 10. You may choose a
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certain number of values, these xi's, any way you wish. But then a certain
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number of values are forced, so that they sum to 10. How many degrees of
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freedom are there? Or in other words, how many values may you choose any way
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you wish. This is tricky.