Five Queens
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Place five queens on a chessboard, such that every square including
those occupied by the queens is under attack.
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Place five queens on a chessboard, such that every square EXCEPT
those occupied by the queens is under attack.
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Find the smallest number of queens needed to attack every square on the
board in the above two conditions for square boards from 2x2 to 7x7.
Source: rec.puzzles.
Solutions were received from Robert Mattson and Philippe Fondanaiche.
Robert's solutions to the first two problems:
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Placing queens at positions (1,2), (2,7), (4,1), (5,3) and (6,6) will
place every position under attack.
- Placing queens at positions (1,2), (1,6), (4,4), (6,4) and (8,4) will
place every position and every queens under attack.
Philippe's solutions:
Notations: a,b,c,d,e,f,g,h for the columns 1,2,3,4,5,6,7,8 for the rows.
1) A possible solution is a5, d5, e5, f5, h1
2) A possible solution is a7, b2, d5, f8, g3
3) Board 2x2 1 queen at a1 in both cases
3x3 1 queen at b2 in both cases
4x4 1) 2 queens at b3, d1 2) 3 queens at c1, b3, d4
5x5 3 queens in both cases: 1) a5, c3, e1 2) a1, b4, d3
6x6 4 queens in both cases: 1) a1, c4, d4, f8 2) b5, c2, e3, f6
7x7 1) 4 queens at a4, d4, e4, f4 2) 5 queens at a7, b3, d1, e6, g3
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