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Posted by Moby Dick
on 14/10/2009, 7:05 pm
Intelligence has reported the approach of an invading army. The border has 9 fortifications (forts) in a line (p1,p2...p8,p9), and there are 11,743 soldiers available. The invader is known to favour flanking moves, so soldiers at forts at the ends of the line have more value than those in the midde. The tactical advisor gives the following value to soldiers at particular forts:
p1: 15, p2: 14, p3: 13, p4: 12, p5: 11, p6: 12, p7: 13, p8: 14, p9: 15
The tactical advisor also imposes the following constraints:
1. The number of soldiers at each fort plus 1/4 the number of soldiers at each fort next to it must not fall below 750 (e.g. p3 + 0.25 p2 + 0.25 p4 >= 750. Forts p1 and p9, of course, each have only one fort next to them)
2. The deployment must be symmetrical (p1=p9, p2=p8, p3=p7, p4=p6)
Deploy your soldiers so as to maximise their value, and specify what that value is (this will be p1*15 + p2*14 + p3*13 + p4*12 + p5*11 + p6*12 + p7*13 + p8*14 + p9*15).
Scoring: 1 point for any valid solution, 2 points for being within 2% of the optimum, 3 points for being within 1%, 4 points for being within 0.5%, and five points for hitting the optimum.
If you need any more motivation, just remember that in this case, the stakes could not be any higher - it is imperative that we hold the line!
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