Topsy Turvy Magic

  Information is the oxygen of the modern age. (Ronald Reagan)

Below is a Topsy-Turvy magic squares. You can easily read the number in each cell but if you turn the page upside down, you can still read the number in each cell. Try it. Print this page for practical

• With the page in its regular position, see if the sum of the numbers in each row, each column, and either diagonal is the same.

• Invert the page and see if a magic square is still formed.

• Check to see whether each of the four quarters of this square forms a magic square.

• Select a number in any cell in one quarter and the number in the corresponding cell in each of the other three quarters.

Example:

Select 689 in the upper left quarter. The number in the corresponding cell in the quarter below is 991; the number in the corresponding cell in the lower right quarter is 816; the number in the corresponding cell in the remaining quarter is 168. The total of these four numbers is 2664. (The cells used in example are reversed in black). Select numbers from 4 other corresponding cells. Add, the total will remain 2664.

• Similarly, add the whole 16 cells of a quarter. The total is 10656. Try another quarters. The total will remain the same i.e 10656.

Note: This Topsy-Turvy Magic Square created by Royal V.Heath and extracted from a Mathematics Course Book, published in some 100 years back, provided by Mr. Hafeez Farooqi. (Thanks for his contribution) 

Prepared by: Muhammad Ajmal Beig Naz

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