## Five Queens

1. Place five queens on a chessboard, such that every square including those occupied by the queens is under attack.
2. Place five queens on a chessboard, such that every square EXCEPT those occupied by the queens is under attack.
3. 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:
1. Placing queens at positions (1,2), (2,7), (4,1), (5,3) and (6,6) will place every position under attack.
2. 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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