Step-by-step Method

Start by putting the number 1 in the middle cell of the top row. Then move diagonally upward to the right to place the next number. Repeat the previous step for the rest of the numbers.

Exceptions: [ Please click the following links in sequence and note the change after each click before proceeding to the next ]

... if you come out of the square at the top of a column,
place the number at the same positon of the bottom row.
... if you come out the square on the right of a row,
place the number at the same position of the extreme left column.
... if the cell is occupied,
place the number directly under the last number you placed.

Regular moves: number 5 and number 6
... if you come out of the square from its top right corner,
place the number directly under the last number you placed.

Another example of Exception #2: number 8

Another example of Exception #1: number 9

Try this method for a 5x5 square. Does it work?

3x3 Magic Square

Step-by-step Method