Saturday,  January 13, 2001
M I N D  G A M E S


Change of heart

Little man Tate is just a bait for Mr Hate who hates every number that makes him slumber. Tate loves all, big or small, even or odd, absolute and mod. Sun has set in the Wild West, when they draw their weapons, and hope for the best.

Before the hatred can evolve, Tate gives Hate a problem to solve. The problem is a matrix of five by five that has a rather magical vibe. The numbers are written all in black because these have been picked from a dusty shack. The magic is that — if you select five numbers, one in every column and every row, the sum of these presents a wonderful show. The sum of the numbers is always the same, and bring matrices a lot of fame.

Hate asks Tate, how did he create the magic square. Tate tells Hate that the explanation is rather fair. Draw a line flat (horizontal) and upright (vertical) and along these, some numbers you write. These numbers control the fate — of corresponding rows and columns, Mr Hate.

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These numbers are written in red because it is a question of butter and bread. Each number in the matrix is the sum of the controlling number above it and to its left (written in red). With five entries selected, one per row and one per column, the sum of the entries is the sum of all the controlling numbers. If you dare, you can make another such square. Even if you change the values of the controlling numbers, the property of the matrix remains unchanged.

Now, write any number of numbers horizontally and the same number of numbers vertically on its left. We have to create a magic square. For the first entry (row 1, column 1) of the square, multiply the number on top with the first number on the left side. For the second entry, (row 1, column 2) multiply the second number on the top with the first number to the left). Complete the square by writing the product of corresponding controlling numbers in the proper slot. When you have this square before you, select one entry from each row and one entry from each column. Multiply these numbers. Repeat the experiment using a different set of numbers. The product will be the same, no matter what combination you choose. You can create another such square with the same property by changing the values on the top or those on the left or both.

We now return to Mr Hate, who is in a dazed state. Now, he is not afraid of digits and his heart is no longer the size of a midget. These numbers change but their property remains the same. Likewise, change yourself with time, but keep your character intact. Every man is a little man Tate, who can easily overcome hate.

— Aditya Rishi

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