Distinct Islands in the Matrix

[TenaliRaman]

1>Given a nxn grid , we colour the grid with 2 colours such that we get the maximum number of distinct islands. What is the maximum number of distinct islands possible for a given nxn grid?
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2>For 3-colours?
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3>Is generalisation possible to m-colours??
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given a 3x3 grid and 2 colours then this colouration *
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1||2||1
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2||2||2
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1||2||1
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gives us 5 islands (the 4 1's and the 1 group of 2's)
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We consider horizontal adjacency,vertical adjacency and also diagonal adjacency when grouping to get islands.

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[TenaliRaman]

has anyone had any progress on this??

All i could judge abt this question was that it was remotely equivalent to the kings problem so the answer must be very much similar. Though a rigorous proof would take the meat!

-- AI