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August 2003
<<July August September>>
Solution:
Part 1:
The setup
K . N B N B N B . . . . . . . . K . K . K . K . . . . . . . . . K . K . K . K . . . . . . . . . N . N B N B N B . R . . . . . .
has value = 1/8 + 6/14 + 7/32 + 9/16 = 299/224 = 1.3348
Part 2:
The setup
N B . . . B B . . . . R . . . . . . R . . . . . B N . . . . B . N . . . . . N . . . . . . . . R . . . . R . . . B B . . . N B .
has value = 4/8 + 8/14 + 5/32 = 275/224 = 1.2277...
Naturally, our solutions do not use queens
Several readers said they have proven optimality, either with an exhaustive search, or by using integer programming.
If you have any problems you think we might enjoy, please send them in. All replies should be sent to: ponder@il.ibm.com