MT 007.02 / SL 266.01
Ideas in Mathematics: The Grammar of Numbers

Exercise

In the following simple third-order magic square the three columns, three rows, and two diagonals each add up to 72.

A) Discuss the construction of the square and how it fits one of the patterns which we have already generated with the series 1...9.
Note in so doing the patterning of the second digits of the numbers.

B) Convert the square into a multiplying magic square, in which the numbers on each of the eight lines multiplied together give the same product.

In doing this you may not change or add to any figures or number symbols in a cell or use an arithmetic sign such as plus (+) or minus (-).

You may, however, move number symbols around any way you like within a cell, e.g. 27 -> 72.

If you hit on the trick, the solution becomes very easy and gratifying, but without it, by trial and error, the solution will seem utterly impossible.

Be sure to discuss how you reached your solution.

Important HINT: The product of each line in the multiplying square is 4096. Given what we are covering now in class, how might that number be significant?

C) Discuss the construction of the resulting multiplying square once you have solved it. How does it relate to the original adding magic square?