### A Magic Square

The "Mathemagician" Art Benjamin is known for mental math capabilities and performances in front of live audiences. Some are on YouTube. In one segment, he draws a 4 X 4 matrix and fills in the top row with the birthdate of a random person. He then fills in the remaining cells such that all the rows and columns add up to the same value. So do the diagonals and the four corners. And so do 5 of the 2 X 2 squares.

He fills the top row with the month, day, tens-digit of the year and one-digit of the year. For example, if the birthdate is 12/12/1944, the start is shown in Figure 1, and the final square is in Figure 2.

Every row and column adds to 32. So do the diagonals and the four corners. The 4 2 X 2 squares that have a corner cell also add to 32. Finally, the 2 X 2 square in the middle adds to 32.

Another example, using the birthdate 1/10/1956. This time the sum is 22.

To construct a magic square, just follow the pattern in Figure 4. If the birth month is January, use the pattern in Figure 5 to avoid negative numbers.