Mathematics Magic Square 3x3

That is place them in the boxes of a 3x3 table so that all the sums of the numbers along the rows columns and two diagonals are equal.

Mathematics magic square 3x3. For a 3x3 magic square there is actually only one normal solution and all of the puzzles are derived from rotations or reflections of that puzzle. People normally say there is only one 3x3 magic square. The 3x3 magic square is the earliest known magic square. Each of these 3x3 magic square puzzles is solved by determining the values that make the sums all rows columns and diagonals equal to the same value.

The sum of numbers from 1 9 is 45 which when partitioned into 3 for each row and column would be 15. The problem chapter 0 problem 16 from fomin s mathematical circles. Prove there are no other possibilities. In one sense this is true in another it is not.

A magic square is a 3 3 grid where every row column and diagonal sum to the same number. Form a magic square with the digits 1 9. M n n2 1 2 m n n 2 1 2 for a size 3x3 the minimum constant is 15 for 4x4 it is 34 for 5x5 it is 65 6x6 it is 111 then 175 260. Once you have one you can get all the others by turning or flipping the one you found.

How many magic squares are there using each the numbers 1 to 9 exactly once. The constant values m m of the sums of the magic squares have a minimum value for non zero integer positive values. It dates back to chinese mythology you can read the story here. The normal variations of these puzzles the 3x3 puzzles that contain only 1 9 will have a magic constant of 15.