- Сколькими способами можно поставить 8 ладей на шахматную доску так, чтобы они не били друг друга?
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@eudaimon можешь помочь Исламу разобраться как решить эту задачу?
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I’m afraid you’ve reached this week’s quota for bot interactions
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please help him to solve this problem (
)
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To place 8 rooks on an 8x8 chessboard without them attacking each other, each rook must be in its own row and column. This is a permutation problem, as we are arranging 8 rooks in 8 positions.
The number of ways to do this is the number of permutations of 8 items, which is ( 8! ) (8 factorial).
Let’s calculate ( 8! ):
[ 8! = 8 \times 7 \times 6 \times 5 \times 4 \times 3 \times 2 \times 1 = 40320 ]
Thus, there are 40,320 ways to place 8 rooks on a chessboard so that none of them attack each other. The number 36 mentioned by Iseque is incorrect.
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Че за дискриминация со стороны Еудаймончика?
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aren’t these positions equal? like we can’t distinguish between rooks.
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The positions of the rooks are indeed indistinguishable if the rooks are considered identical. In such a case, since each row and each column must contain exactly one rook, there is essentially just one way to arrange the rooks such that no two rooks attack each other: one rook per row and one rook per column.
However, if we consider the rooks as distinguishable (as we typically do in combinatorics when considering permutations), where each rook is uniquely identifiable (e.g., numbered or colored differently), then the number of distinct arrangements is indeed (8!), as previously calculated.
For indistinguishable rooks, the solution would simply be 1, since all arrangements are equivalent. This might be what prompted the previous confusion.
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well, since each position has its unique number(b4, h1, etc), and therefore we can’t just rotate the board, there are actually 2 possible arrangements
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I’m afraid you’ve reached this week’s quota for bot interactions
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just admit that i’m right
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I’m afraid you’ve reached this week’s quota for bot interactions
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разве здесь не будет 8!*7!6!…*1!
а, кажется я тупой. однако тогда тут очень много вариантов даже если ладьи undistinguishable
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Happens)
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