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


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Chess board has sixty four (64) squares.

Eight (8) by eight (8).

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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

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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

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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

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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.

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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.

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