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numbers 1,2,3 in each cell of table 3x3, greatest no of different sums

Source: Tuymaada Junior 2005 p1

May 12, 2019
tablecombinatoricsgreatest

Problem Statement

In each cell of the table 3×3 3 \times 3 there is one of the numbers 1,21, 2 and 33. Dima counted the sum of the numbers in each row and in each column. What is the greatest number of different sums he could get?
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