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Integer Sequences to Represent Solutions to the Eight Queens Puzzle
It's my delight to share with you my discovery that if all sixty-four squares of the chess board are numbered from one to sixty-four, starting from square a1 to square h8, and the eight queens are numbered according to their placements in the squares, all 92 distinct solutions can be represented by 92 integer sequences, each queen placement represents a term. And for all 92 sequences, the sum of all eight terms in each sequence is 260. Following are the twelve integer sequences that represent the twelve unique solutions out of possible 92 distinct solutions. If you see an error in this list, please let me know. Paul
| Sol |
Sequence |
Total |
| Q1 |
8,10,20,25,39,45,51,62 |
260 |
| Q2 |
8,10,21,27,33,47,52,62 |
260 |
| Q3 |
3,16,20,31,33,46,50,61 |
260 |
| Q4 |
5,16,20,25,39,42,54,59 |
260 |
| Q5 |
4,16,17,29,39,42,54,59 |
260 |
| Q6 |
6,16,18,28,33,47,53,59 |
260 |
| Q7 |
4,16,21,27,33,47,50,62 |
260 |
| Q8 |
5,10,20,30,40,43,49,63 |
260 |
| Q9 |
4,16,17,27,38,42,55,61 |
260 |
| Q10 |
4,14,24,26,39,41,51,61 |
260 |
| Q11 |
4,10,24,29,39,41,51,62 |
260 |
| Q12 |
3,14,24,25,37,47,50,60 |
260 |
Copyright © 1996-2004 Paul B. Muljadi. All
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