In a magic NxN square, numbers from 1 to Nē are set so the numbers in each row, column, or major diagonal, have the same sum: the "magic constant".
What is the value of this constant, as a function of N?
(In reply to
re(2): Spoiler by Ken Haley)
The answer to this one is so obvious that I was looking for something to justify the difficulty level. :)
Clearly the sum of the N equal row sums equals the sum of all the
elements, since each element appears only once. Summing
consecutive numbers is a standard process for which Gauss
supposedly figured out the easy method when he was 8 years old or
so: Write the numbers in order and underneath them write them in
reverse order. Twice the sum of the N^2 numbers is then N^2 times
1+N^2, and 1/Nth of the sum is the magic number.
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Posted by Richard
on 2005-02-25 17:04:07 |
re(3): Spoiler
