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August 2003

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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.


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