Master the Magic Square: Tips for Solving the 3x3 Puzzle in Just 4 Hours

In summary, the conversation discussed a problem involving placing numbers in a 3 x 3 square where the numbers in the top row minus the numbers in the 2nd row equal the numbers in the 3rd row. The conversation also mentioned a potential solution using the technique of borrowing from the tens column, and the possibility of not being able to solve the problem without borrowing. Finally, it was mentioned that there are 336 solutions if borrowing is allowed.
  • #1
janvianish
3
0
HI

In a square 3 x 3 using the numbers 1 to 9 once only put the numbers so that:
the numbers on the top row minus the numbers in the 2nd row = the numbers on the 3rd row.

trying this for about 4 hrs and am always 1 number out.
 
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  • #2
Um.. one possible answer:

846, 327 and 519

It was rather trial and error though, and departing from that I should be getting the first digits to be subtracted requiring borrowing from the tens column.
 
  • #3
hi thanks for this but i do not think we can borrow from another column
 
  • #4
Unknown008's neat trick of borrowing from the tens column is the only way to solve this problem. If borrowing is not allowed then the problem has no solution.

In fact, each number in the top row would then have to be the sum of the two numbers below it. But an odd number must be the sum of an odd number and an even number; and an even number is either the sum of two even numbers or the sum of two odd numbers. That means that each column must contain either two odd numbers or no odd numbers. Therefore the total number of odd numbers in the square must be even. But there are five odd numbers in the set 1, ..., 9, and five is not an even number. So there is no possibility to fill the square in the required way (except by using the borrowing trick).
 
  • #5
If borrowing is allowed, then exhaustive search shows that there are 336 solutions.
 
  • #6
thanks to all for your help...
 

Related to Master the Magic Square: Tips for Solving the 3x3 Puzzle in Just 4 Hours

1. What is a magic square?

A magic square is a square grid filled with distinct numbers in such a way that the sum of the numbers in each row, column, and diagonal is the same.

2. How do I create a magic square?

There are various methods to create a magic square, but one of the most common methods is to start with the number 1 in the middle of the top row, then fill in the numbers in a specific pattern, making sure that each number only appears once and that the sum of each row, column, and diagonal is the same.

3. What are some properties of magic squares?

Magic squares have several interesting properties, such as the fact that the sum of the numbers in any row, column, or diagonal is called the "magic constant". Additionally, the number of possible magic squares increases significantly as the size of the square increases.

4. How can I check if a square is a magic square?

To check if a square is a magic square, you can simply add up the numbers in each row, column, and diagonal and see if they all equal the same sum. If they do, then the square is a magic square.

5. Is there a specific order in which the numbers must be placed in a magic square?

Yes, there are specific rules for placing the numbers in a magic square. One common rule is the "Knight's tour" method, where the numbers are placed in a specific pattern that resembles the movement of a knight in a game of chess. However, there are other methods as well, such as the "Siamese method" or the "De la Loubère method".

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