Dec 112012

Imagine you have infinite number of Queens.

Find the minimum number of queens required so that every square grid on the chess board is under the attack of a queen.

Arrange this minimum no. of Queens on a chess board.

**Solution:**

Easiest solution is to put a queen in all the squares (64 queens required). We can obviously do much better than this.

**Queen @ every diagonal **

If we put one queen at each diagonal cells (i.e put a queen when i==j). Then also all the cells in the chess-board will be under attack.

**Improving the above solution:**

There will be more than one solution to the problem (If you rotate the chessboard, you will get another solution – if queens are non-symmetric).. Below is a solution with 5 queens: