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ASU 435 All Soviet Union MO 1986 nxn table with +1 and -1, man and max wanted

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August 7, 2019
combinatoricsminimummaximumsquare tabletable

Problem Statement

All the fields of a square n×nn\times n (n>2) table are filled with +1+1 or −1-1 according to the rules:
At the beginning −1-1 are put in all the boundary fields. The number put in the field in turn (the field is chosen arbitrarily) equals to the product of the closest, from the different sides, numbers in its row or in its column.
a) What is the minimal
b) What is the maximal
possible number of +1+1 in the obtained table?
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