0:00:00.200,0:00:05.501 Let's pick any number in here. Let's say 5. Can we choose this number and still 0:00:05.501,0:00:12.690 have this sum to 9, and still have these columns sum to 9? Yeah. Let's say 3. 0:00:12.690,0:00:17.602 So together those make 8, and that means this one is forced it has to be 1. 0:00:17.602,0:00:24.500 Okay, can we pick a value here. Yeah, let's say 8. So those sum to 13, which 0:00:24.500,0:00:30.130 means that this value is forced. This has to be negative 4, and then can we 0:00:30.130,0:00:36.460 pick a value here, and have this row and this column still sum to 9? Yeah, 0:00:36.460,0:00:41.467 let's say 7. Now if this column has to sum to 9, then this entry's forced, it's 0:00:41.467,0:00:47.651 negative 1. And as you can see, this entry's forced too, this adds to 15, so to 0:00:47.651,0:00:54.740 add to 9, this should be negative 6. And this entry's forced as well, this has 0:00:54.740,0:01:00.711 to be 14. Then both this column and this row sum to 9. So in this case there 0:01:00.711,0:01:05.829 are 4 degrees of freedom. But if we have an n by n table, in this case this is 0:01:05.829,0:01:11.950 a 3 by 3 table. This is a 4 by 4 table. Then we would be able to chose all of 0:01:11.950,0:01:18.260 these entries but then these ones would be forced. This number of tiles is n 0:01:18.260,0:01:24.760 minus 1. And this number of tiles is also n minus 1. So the total number that 0:01:24.760,0:01:31.710 we can choose is n minus 1 squared. So here in this 3 by 3 table, we were able 0:01:31.710,0:01:39.262 to choose 2 times 2. In this 4 by 4 table, we were able to choose 3 times 3. So 0:01:39.262,0:01:44.336 when we have an n by n table, we can choose n minus 1 times n minus 1, or just 0:01:44.336,0:01:47.724 n minus 1 squared.