What is the minimum number of queens required on a chess board such that all squares are attacked?


Selene

Recommended Posts

Chess board has sixty four (64) squares.

Eight (8) by eight (8).

Link to comment
Share on other sites

Chess board has sixty four (64) squares.

Eight (8) by eight (8).

I can do it with six, but that's too easy so my answer is five.

--Brant

Six is the best I can do so far.

Ba'al Chatzaf

Link to comment
Share on other sites

Chess board has sixty four (64) squares.

Eight (8) by eight (8).

Now vary the problem a bit. Identify the top edge with the bottom edge and the left edge with the right edge and you have a toroidal chess board. What is the minimum number of queen required to cover it?

Ba'al Chatzaf

Link to comment
Share on other sites

Chess board has sixty four (64) squares.

Eight (8) by eight (8).

I can do it with six, but that's too easy so my answer is five.

--Brant

Five will do it. See http://mathworld.wolfram.com/QueensProblem.html

Ba'al Chatzaf

Link to comment
Share on other sites

Five is correct.

There is a different configuration in the solve that I have than what Ba'al showed which is WQ1, WQ 4, 5, 6, and 7.

For other uses, see Toroid (disambiguation). 220px-Toroid_by_Zureks.svg.png magnify-clip.png A toroid using a square. 220px-Torus.png magnify-clip.png A torus is a type of toroid. 37px-Wiktionary-logo-en.svg.png Look up toroid in Wiktionary, the free dictionary. In mathematics, a toroid is a doughnut-shaped object, such as an O-ring. Its annular shape is generated by revolving a geometrical figure around an axis external to that figure.[1] When a rectangle is rotated around an axis parallel to one of its edges then a hollow cylinder (resembling a piece of straight pipe) is produced.

If the revolved figure is a circle, then the surface of such an object is known as a torus.

Link to comment
Share on other sites

Chess board has sixty four (64) squares.

Eight (8) by eight (8).

Now vary the problem a bit. Identify the top edge with the bottom edge and the left edge with the right edge and you have a toroidal chess board. What is the minimum number of queen required to cover it?

Ba'al Chatzaf

Four.

Link to comment
Share on other sites

Create an account or sign in to comment

You need to be a member in order to leave a comment

Create an account

Sign up for a new account in our community. It's easy!

Register a new account

Sign in

Already have an account? Sign in here.

Sign In Now