WEBVTT
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Let's pick any number in here. Let's say 5. Can we choose this number and still
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have this sum to 9, and still have these columns sum to 9? Yeah. Let's say 3.
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So together those make 8, and that means this one is forced it has to be 1.
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Okay, can we pick a value here. Yeah, let's say 8. So those sum to 13, which
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means that this value is forced. This has to be negative 4, and then can we
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pick a value here, and have this row and this column still sum to 9? Yeah,
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let's say 7. Now if this column has to sum to 9, then this entry's forced, it's
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negative 1. And as you can see, this entry's forced too, this adds to 15, so to
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add to 9, this should be negative 6. And this entry's forced as well, this has
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to be 14. Then both this column and this row sum to 9. So in this case there
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are 4 degrees of freedom. But if we have an n by n table, in this case this is
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a 3 by 3 table. This is a 4 by 4 table. Then we would be able to chose all of
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these entries but then these ones would be forced. This number of tiles is n
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minus 1. And this number of tiles is also n minus 1. So the total number that
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we can choose is n minus 1 squared. So here in this 3 by 3 table, we were able
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to choose 2 times 2. In this 4 by 4 table, we were able to choose 3 times 3. So
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when we have an n by n table, we can choose n minus 1 times n minus 1, or just
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n minus 1 squared.