Magic square
Many people know the concept of Magic Square (MK) - a square table N x N filled with natural numbers from 1 to N ^ 2 in such a way that the sum of the numbers in each row, diagonal and column is equal to ... N * (N ^ 2 + 1) / 2.
At school I was interested in mathematics and noticed interesting properties of MK with odd N. Although, of course, these properties may already be known, I didn’t go into it, and I don’t have any idea where and to whom it can be useful, I just set it up, I was surprised .
So, we have the MC of digit capacity, for example, N = 7:
If we find in this MK all numbers that are multiples of 2 and mark them with a red marker, then we get a picture:
similarly, multiples of 3:
... multiples of 5:
... multiples of 7:
Immediately evident obvious pattern. For other odd dimensions N, we obtain similar laws.
At school I was interested in mathematics and noticed interesting properties of MK with odd N. Although, of course, these properties may already be known, I didn’t go into it, and I don’t have any idea where and to whom it can be useful, I just set it up, I was surprised .
So, we have the MC of digit capacity, for example, N = 7:
If we find in this MK all numbers that are multiples of 2 and mark them with a red marker, then we get a picture:
similarly, multiples of 3:
... multiples of 5:
... multiples of 7:
Immediately evident obvious pattern. For other odd dimensions N, we obtain similar laws.
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Source: https://habr.com/ru/post/123061/
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