> Let elaborate a little more on this. We want one number for each cells :
> nums = {n1, n2, n3, ..., n81}
>
> And we want the following properties :
>
> for any a, b in nums :
> (a + b) / 2 is in nums --> a == b
> for any a, b, c in nums :
> (a + b + c) / 3 is in nums --> a == b == c
> for any a, b, c, d in nums :
> (a + b + c + d) / 4 is in nums --> a == b == c == d
>
> If we have this we are sure to don't have problems like you pointed.
> Using brute force search, I've produced the following sequence of
> numbers :
>
> [17, 18, 21, 30, 49, 86, 134, 274, 590, 1061, 1348, 2301, 3005, 4805,
> 7609, 11157, 17802, 19393, 29046, 31538, 41442, 49154, 74823, 97358,
> 134625, 148826, 217801, 234930, 294657, 402550, 452686, 610274,
> 726514, 885190, 1040877, 1070361, 1337862, 1611001, 1829345, 1962193,
> 2308061, 3007701, 3133837, 4007989, 4727218, 4883797, 5546029, 7454733,
> 8548661, 9547305, 11552366, 13177582, 13697142, 14689461, 15538838,
> 15733662, 21054617, 22691377, 24433197, 27274934, 31994414, 35217106,
> 37507258, 41114134, 45045090, 47089386, 57357330, 62400606, 68297193,
> 75036946, 83039110, 96477718, 110160994, 119390498, 122575210,
> 148912497, 156351446, 168096257, 176942297, 194310098, 211199842]
>
-- snip --
>
> And the second problems is that this solution doesn't scale well. On
> 19x19 you need 361 numbers in your list, so even if you find a list like
> this, I doubt that you can sum up the value of all the pseudo liberties
> of a big group without overflowing an unsigned and you have to switch
> to bigger int like int 64.
Based on more recent emails, this may not be useful anymore, but I
have a list of 361 32-bit numbers that satisfy these properties in
case anyone is interested.
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