perplexus.info :: Games : Smallest Square Chessboard

Smallest Square Chessboard (Posted on 2023-01-23)

Place precisely four Bishops and four Knights in a square chessboard of any size such that:

Each Bishop is attacking exactly 2 Knights, but no Bishop.
Each Knight is attacking exactly 2 Bishops but no Knights.

Determine the smallest chessboard that is required to achieve this.

Submitted by K Sengupta

Rating: 4.0000 (1 votes)

Solution: (Hide)

In a 4x4 chessboard, we can have this placement:
+---+---+---+---+ | | B | B | | +---+---+---+---+ B -> Bishop | N | | | N | N -> Knight +---+---+---+---+ | N | | | N | +---+---+---+---+ | | B | B | | +---+---+---+---+
This satisfies all the given conditions.
Thus, the required smallest dimension of the square chessboard is 4x4.
For a more detailed explanation, refer to the solution submitted by Jer in this location.

Comments: ( You must be logged in to post comments.)

Subject	Author	Date
No Subject	jaydeniaz	2023-10-20 05:16:01
Solution	Jer	2023-01-23 12:49:31

Please log in:

Login:
Password:
Remember me:

Sign up! \| Forgot password

Search:

Search body:

Forums (0)
Newest Problems
Random Problem
FAQ | About This Site
Site Statistics
New Comments (5)
Unsolved Problems
Top Rated Problems
This month's top
Most Commented On

Chatterbox:


perplexus dot info