MathDB

We consider

5 \times 5

tables containing a real number in each of the

25

cells. The same number may occur in different cells, but no row or column contains five equal numbers. Such a table is balanced if the number in the middle cell of every row and column is the average of the numbers in that row or column. A cell is called small if the number in that cell is strictly smaller than the number in the cell in the very middle of the table. What is the least number of small cells that a balanced table can have?

Problem Statement