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| Math Mojo - Making Math Meaningful |
This was the question:
Can you create a 5-cell x 5-cell magic square, in which all the even number from 2 to 50, inclusive, are used, and the sum of all rows, columns and diagonals are 130?
Professor Homunculus' answer:
The logic of answering it might go something like this:
- Do I know how to create a normal 5-cell x-5 cell magic square? I do.
- I know that it usually starts with 1, and has 25 cells, so it must use the number from 1 to 25, inclusive. It is easy to see that if you use only even numbers, the square will fulfill the first part of the question.
- Do I remember the sum of columns, rows and diagonals of a normal magic square? Well, I happen to, and it is 65.
What relationship does 65 have to 130? It is half. So I can imagine that if I double the numbers in a regular magic square, I would end up with double the sums. (This would have been an example of a rational way to figure out the problem).- If I had not remembered the sum of a normal 5 x 5 magic square, I could have easily just made the square, and added up the columns to see if totaled 65.(This would have been and example of an empirical way to tackle the problem).
Either way, I would have found out that if I simply did a normal 25-cell magic square, but doubled the digits, I would have fulfilled all the conditions of the problem. Below you have the final product.
Want another interesting magic square? click here
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