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You are trying to solve the famous N queens problem. You broke one of the queens from your chess pieces collections. Now, you have created the following puzzle:

You are given an N*N chessboard. Is it possible to place N-1 queens on it in such a way that no pair of queens is attacking each other?

Two queens are attacking each other if at least one of the following conditions is true:

They share the same row They share the same column They share the same diagonal You are given a single integer N. Print any possible configuration in the format below. It is guaranteed that there is always an answer

for example N=4. one of the possible answer is

* . . .
. . * .
. . . .
. * . .
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    $\begingroup$ Of course N-1 queens are possible: just pick a solution of N queens then remove one of them. $\endgroup$ – athin May 2 at 5:33
  • $\begingroup$ @athin but how to print that pattern $\endgroup$ – sukesh May 2 at 5:33
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    $\begingroup$ Printing patterns makes me wonder.. Is it from a programming contest, in some sense? $\endgroup$ – athin May 2 at 5:42
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    $\begingroup$ In that case, could you give first which contest does this come from? Otherwise the question might be closed as a result of not having a proper attribution. I also want to help, but if this is from an on-going competition then we need to wait until it's over too. $\endgroup$ – athin May 2 at 5:48
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    $\begingroup$ If you need help with constructing a program to solve this problem, then it would be better to ask on a programming site, not on a puzzle site. You can find many programs for the standard N-queens problem very easily. Once you understand how those programs work, try to adapt one them to this problem. $\endgroup$ – Jaap Scherphuis May 2 at 7:22
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Note that the $N$ queens problem is always solvable except for $N=2$ and $3$, so by removing any queen from the solution we get a valid $N-1$ queens solution. For $N=2$, it's trivial to place $2-1=1$ queen into any square. For $N=3$, it's sufficient to place $3-1=2$ queens at a distance of a knight's move, so they would not attack each other.

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  • $\begingroup$ can u help me how to print patterns $\endgroup$ – sukesh May 2 at 5:47
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    $\begingroup$ @trolley813 Note that your solution method is not necessarily reversible, so there will usually also be solutions to the N-1 queens problem that cannot be generated in this way. The 4x4 example in the problem statement is one example. $\endgroup$ – Jaap Scherphuis May 2 at 7:35
  • $\begingroup$ Yes, you're right. It's sufficient but not necessary to build a full N-queen solution, there are positions with N-1 queens where it's impossible to add the Nth queen. $\endgroup$ – trolley813 May 2 at 7:38

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