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How many squares can you have between n points?(impossibility results)How much value do you need to give a square with value 1 to each agent?(possibility results)
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With (value+1) points you can have at least (agents) squares.For (squares+1) agents you need a value of at least (points).
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points /// walls0 (plane)1 (half plane)2 (quart. plane)3 (open square)4 (square / 2-fat rectangle)agents /// walls0 (plane)1 (half plane)2 (quart. plane)3 (open square)4 (square / 2-fat rectangle)
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100000111111
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211111222334
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322111334556
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4322214467..97..118..12
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543222568..9
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64333267..89..12
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74..543..42..42..378..1010..18
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84..643..42..42..389..1212..24
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94..74..63..62..62..4910..15
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104..84..63..72..41012..20
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114..94..63..51112..20
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124..94..73..51212..20
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- LB -- LB -~5n/4~3n/22n-12n-12n
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- UB -~4p/52(p-1)/3~p/2~p/2(p-1)/2- UB -4n-28 (12+)4n-14 (6+)4n-7 (3+)4n-5 (2+)4n-4 (2+)
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