An n-by-n magic square is an n-by-n grid into which the numbers 1, 2, . . . , n 2 are placed, once each. The “magic” is that each row, column, and diagonal must be filled with numbers that have the...

An n-by-n magic square is an n-by-n grid into which the numbers 1, 2, . . . , n 2 are placed, once each. The “magic” is that each row, column, and diagonal must be filled with numbers that have the same sum. For example, a 3-by-3 magic square is shown in Figure 5.13. Conjecture and prove a formula for what the sum of each row/column/diagonal must be in an n-by-n magic square.