MAGIC SQUARES - III

Abstract

1. Magic square: A square divided into the equal number of small squares both horizontally (i.e. length-wise) and vertically (i.e. breadth-wise) and filled up with positive whole numbers, in such a way that when the numbers in the different rows—vertical, horizontal and diagonal—are added, the same sum is obtained. While filling the small squares, no number should be repeated. 4 9 2 3 5 7 8 1 6 2. A house 2. A house2. A house: Each small square is called a house. 3. Horizontal and vertical rows of houses: Houses lying in the same horizontal row, running from the left to the right, form a horizontal row of houses. Houses lying in the same vertical row, running from top to bottom, form a vertical row of houses. The horizontal rows of houses are numbered from top downwards and the vertical rows of houses are numbered from the left to the right. The houses themselves are numbered from left to right starting from the first horizontal row of houses and in the same order down to the end of the last horizontal row. Note: Any corner house may be called House 1 and the numbering may proceed in either direction from this house. The different ways of numbering in a four-house squares are shown on the next page. 4. A series 4. A series4. A series: An arithmetical series is in short called a Series (Later, what I prefer to call a compound series is introduced)