Construction 2

Discrete Mathematics Level 3

In the seventeenth century, de la Loubere found a technique for constructing magic squares of order \(n\), where \(n\) is odd. The method (as stated in Brualdi) is described as follows:

  1. First, a 1 is placed in the middle square of the top row.
  2. The successive integers are then placed in their natural order (i.e. 2, 3, 4, ...) along a diagonal line that slopes upward and to the right, with the following modifications:
  • When the top row is reached, the next integer is put in the bottom row as if it came immediately above the top row.
  • When the right-hand column is reached, the next integer is put in the left-hand column as if it had immediately succeeded the right-hand column.
  • When a square that has already been filled is reached or when the top right-hand square is reached, the next integer is placed in the square immediately below the last square that was filled.

Now, construct a magic square of order 11 using the above method. Among the numbers in the right-hand column, how many are odd?


Problem Loading...

Note Loading...

Set Loading...