Mean Grids: (i) Fill the grid with 9 distinct numbers such that the average along each row, column, and diagonal is 10. (ii) Can we fill the grid by changing a few numbers and still get 10 as the average in all directions?
One possible arrangement with 9 distinct numbers where each row, column, and diagonal has average 10: Place numbers such that each line sums to 30. Example: Top row: 16, 2, 12; Middle row: 6, 10, 14; Bottom row: 8, 18, 4.
Yes, multiple arrangements are possible. Different sets of 9 distinct numbers can be used as long as each row, column, and diagonal sums to 30.
Explanation
(i) Each row/column/diagonal must sum to 30 for the average to be 10. (ii) The constraint is that each line must sum to 30, which can be achieved with various number combinations.