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Self-describing tables

Source: 2019-20 International Dürer Competition , Category E, P5

August 19, 2020
combinatoricscountingTables

Problem Statement

We call a table of size n×nn \times n self-describing if each cell of the table contains the total number of even numbers in its row and column other than itself. How many self-describing tables of size a) 3×33 \times 3 exist? b) 4×44 \times 4 exist? c) 5×55 \times 5 exist? Two tables are different if they differ in at least one cell.
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