Sudoku Diagonal
Help Solving this math puzzle!!?
I need help solving a puzzle- let me see if I can explain it.
The puzzle is sort of like a Sudoku puzzle- but it consists of the numbers 1 through 16. The grid is a 4 x 4 grid and each number can only be used once.
So you have the numbers 1,2,3,4,5,6,7,8,9,10,11,12,13,14,15 and 16 and each can only be used once.
Here are the other rules:
Each of the 4 rows must equal the same number (which is unknown at this point)
Each of the 4 columns rows must equal the same number as the rows. So the product is the same all the way through.
Along with the columns and rows, the diagonals must also equal the same number as the columns and rows.
Not only those, but also the four outermost corners AND the four innermost corners must also equal the same number.
So, there are 6 different ways that they all have to equal the SAME number.
Either an answer or the formula (if known) will help!! Thank you!!!!!!!
This is an example of a 4 by 4 magic square.
One well known solution is:
[9.....6.....3....16]
[4....15...10... 5]
[14...1.....8...11]
[7....12...13...2]
This satisfies all your criteria.
The total of each line is n(n² + 1) / 2 where n is the width of the square.
Here n = 4 so that
n(n² + 1) / 2 = 4(16 + 1) / 2
= 2 * 17
= 34
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