If you place 8 queens on a 8x8 grid such that no two queens threaten each other. Find the number of distinct solutions ignoring reflections and rotation.
Question 9Answer

a.
24

b.
45

c.
12

d.
92

The problem you're referring to is a famous combinatorial problem called the "Eight Queens Puzzle," where the objective is to place 8 queens on an 8×8 chessboard such that no two queens can attack each other (i.e., no two queens share the same row, column, or diagonal).

There are **92 distinct solutions** to the Eight Queens Puzzle when considering all rotations and reflections. However, if we ignore rotational and reflectional symmetries, the number of distinct solutions is **12**.

So, the correct answer is:

**c. 12**

Would you like more details on how the solutions are counted or the approach to solving the Eight Queens problem?

Here are 5 related questions you might find interesting:
1. How can the backtracking algorithm be applied to solve the Eight Queens Puzzle?
2. What is the difference between distinct solutions and equivalent solutions in the context of the Eight Queens Puzzle?
3. How many solutions exist for an n-queens problem when n > 8?
4. What is the role of symmetry in reducing the number of distinct solutions in the Eight Queens Puzzle?
5. Can the Eight Queens problem be extended to other chess pieces, like rooks or knights?

**Tip**: Symmetry reduction in combinatorial problems can dramatically reduce the number of cases you need to consider, saving both time and computation.

If you place 8 queens on a 8x8 grid such that no two queens threaten each other. Find the number of distinct solutions ignoring reflections and rotation.

Explore the famous Eight Queens Puzzle, where 8 queens are placed on an 8x8 chessboard so that no two threaten each other. Learn about symmetry reduction and how to find 12 distinct solutions, ignoring reflections and rotations. Suitable for Grades 9-12, with a focus on combinatorics and algorithmic thinking.

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