Question

На доске 10 x 10 стоит 6 ладей, никакие две из которых не бьют друг друга. Сколькими способами на эту доску можно добавить еще две ладьи так, чтобы никакие две ладьи на доске не били друг друга (расстановки ладей отличаются друг от друга только в случае, если отличается набор клеток, которые эти ладьи занимают)?

Answer 1

Скорее всего будет 5 способов.
1) Длина ладьи 1 клетка(все влезают)
2) Длина ладьи 2 клетки (влезают)
3,4,5) Длина ладьи 3,4 и 5 (влезают)
6) Длина ладь 6 клеток (1 ладья не влезает)

Answer 2

Calculating the Number of Ways to Add Two Rooks

To calculate the number of ways to add two rooks to a 10x10 chessboard such that no two rooks attack each other, we can use the concept of permutations and combinations.

Step 1: Initial Rook Placement Given that there are already 6 rooks on the 10x10 chessboard, we need to calculate the number of ways to place the additional two rooks without them attacking each other.

Step 2: Calculation The number of ways to place the additional two rooks can be calculated using the formula for combinations. The formula for combinations is given by: $$C(n, r) = \frac{n!}{r!(n-r)!}$$ Where: - n is the total number of items - r is the number of items to choose

In this case, n = 100 (total number of cells on the 10x10 chessboard) and r = 2 (number of rooks to be placed).

Using the combination formula, we can calculate the number of ways to place the additional two rooks on the chessboard.

Step 3: Calculation Using the combination formula, we can calculate the number of ways to place the additional two rooks on the chessboard: $$C(100, 2) = \frac{100!}{2!(100-2)!}$$

Answer

The number of ways to add two rooks to the 10x10 chessboard such that no two rooks attack each other is 4950.