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Puzzle # 328_Magic Squares
29-Aug-14
Views : 710
Rated 5.0 by 1 User
 
Bharath, the mathematics genius and professor, asked his students to identify the following table:


Vicky (instantly raising his hand): Come on sir, we all know this is a Magic Square. The sum of the numbers in any row, column or diagonal adds up to 15. Also, a magic square of this type can be created using any 9 numbers in an arithmetic sequence.
Bharath: Well said Vicky. That was very informative for all of us. Now have a look at this and tell me what you can find in it.


Bharath (after a 5 minute silence): Looks like I’ll have to reveal the answer this time.
Nithin: I got it sir. The previous one was a Sum Magic Square, whereas this one is a Difference Magic Square.
Bharath: Now that’s more like it Nithin. Tell me more.
Nithin: Take any row, column or diagonal. Subtract the 1st number from the 2nd and subtract the result from the 3rd number. You get the result 5 in each case. For instance, the second row gives you 7 − (5 − 3) = 5 and the second column gives 9 – (5 – 1) = 5; and so on.
Bharath: Excellent work Nithin. I’m impressed. Anyway guys, get ready for the next challenge. This is your homework. I want all of you to create a Multiplication Magic Square. Choose any set of nine numbers that you want, and create a Magic Square based on multiplication, similar to the one on Addition, i.e., the product of the numbers in any row, column or diagonal must be the same. Also, this should be the smallest multiplication square possible.
Vicky: This seems tough sir. A few clues on this would help us.
Bharath: Alright Vicky, the 9 numbers you choose, must be the only 9 factors of a given number. I can’t tell you more than this.

Can you help the students create the Multiplication Magic Square?
 Solution




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