This is the sort of math/logic problem that can keep you up all night: Imagine a blank sudoku grid. You can place the numbers 1-9 anywhere in the grid, without repeating. After you place them, you can ask to check if the placement is correct. A line of numbers appears at the bottom and right, which indicate if the numbers are correct/in the right line but in the wrong place.
Say, for example, you place a apos;6apos; in the upper left square. You check it, and the bottom reads 0/0, and the right of the 6 reads 0/0, indicating that 6 does not appear anywhere in the first column down or the first column across. Therefore, it must be in one of the bottom four squares. And of course, any other numbers you placed in the first column are wrong, as is the first row.
Simple enough concept. The question is, assuming you make no mistakes in placing the numbers after checking once(the numbers are all in a logical position, though not necessarily correct, according to the information you are given), how many times will it take to come up with the correct placement?
My apos;guessapos;, after doing this 30+ times? Two turns. That is, place the numbers 1-9 randomly, check them, place and check once more, and you should be able to get the right answer. The question is, will it always work that way? Is there a way to prove it? And is there a set number of apos;logicalapos; combinations after the first check?
I donapos;t know the answer, and I donapos;t really remember much about permutations and combinations... Theoretically, you could guess the correct answer on the first or second turn, but itapos;s pretty unlikely.
Times like this, I wish I still lived in Nac, if only cause I could totally bother my calculus teacher with this.
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