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N-queens benchmark and the HP-17BII

Posted by Thomas Klemm on 7 Feb 2011, 5:48 a.m.

## Equation for the 8-queens problem

```QUEENS:
Q=A+B+C+D+E+F+G+H+ (I:1:8:1: (J:1:8:1:
IF(I<>J AND SQ(I-J)<>1: (K:1:8:1:
IF(I<>K AND SQ(I-K)<>4
AND J<>K AND SQ(J-K)<>1: (L:1:8:1:
IF(I<>L AND SQ(I-L)<>9
AND J<>L AND SQ(J-L)<>4
AND K<>L AND SQ(K-L)<>1: (M:1:8:1:
IF(I<>M AND SQ(I-M)<>16
AND J<>M AND SQ(J-M)<>9
AND K<>M AND SQ(K-M)<>4
AND L<>M AND SQ(L-M)<>1: (N:1:8:1:
IF(I<>N AND SQ(I-N)<>25
AND J<>N AND SQ(J-N)<>16
AND K<>N AND SQ(K-N)<>9
AND L<>N AND SQ(L-N)<>4
AND M<>N AND SQ(M-N)<>1: (O:1:8:1:
IF(I<>O AND SQ(I-O)<>36
AND J<>O AND SQ(J-O)<>25
AND K<>O AND SQ(K-O)<>16
AND L<>O AND SQ(L-O)<>9
AND M<>O AND SQ(M-O)<>4
AND N<>O AND SQ(N-O)<>1: (P:1:8:1:
IF(I<>P AND SQ(I-P)<>49
AND J<>P AND SQ(J-P)<>36
AND K<>P AND SQ(K-P)<>25
AND L<>P AND SQ(L-P)<>16
AND M<>P AND SQ(M-P)<>9
AND N<>P AND SQ(N-P)<>4
AND O<>P AND SQ(O-P)<>1:
L(A:I)xL(B:J)xL(C:K)xL(D:L)xL(E:M)xL(F:N)xL(G:O)xL(H:P)/0
:0)):0)):0)):0)):0)):0)):0)))
```

## Solution

Solve the equation for Q. After a while (3:29) you get an error message:

```SOLUTION NOT FOUND
```

Now you can recall the solution in the variables A-H. The result { 1, 5, 8, 6, 3, 7, 2, 4 } corresponds to the following configuration:

```    A   B   C   D   E   F   G   H
+---+---+---+---+---+---+---+---+
8 |   |   | # |   |   |   |   |   |
+---+---+---+---+---+---+---+---+
7 |   |   |   |   |   | # |   |   |
+---+---+---+---+---+---+---+---+
6 |   |   |   | # |   |   |   |   |
+---+---+---+---+---+---+---+---+
5 |   | # |   |   |   |   |   |   |
+---+---+---+---+---+---+---+---+
4 |   |   |   |   |   |   |   | # |
+---+---+---+---+---+---+---+---+
3 |   |   |   |   | # |   |   |   |
+---+---+---+---+---+---+---+---+
2 |   |   |   |   |   |   | # |   |
+---+---+---+---+---+---+---+---+
1 | # |   |   |   |   |   |   |   |
+---+---+---+---+---+---+---+---+
```

## References

Edited: 7 Feb 2011, 6:27 a.m.