Magic squares 4 x 4 pdf

It is said that albrecht durer a german painter, engraver, mathematician, and theorist from nuremberg had made one such magic square in 1514. Pdf generalized form of a 4x4 magic square researchgate. The order4 pandiagonal magic square used as a pattern to place the order3 squares. Therefore, 3 x 16 x 4 x 2 384 regular, order four, pan magic squares can be derived from these three possible squares. For a 3x3, 4x4, 5x5, 6x6, 7x7, 8x8, 9 x 9, and 10 x 10 magic squares the sum of the integers in any row, column, or diagonal will be 15, 34, 65,111, 175, 260, 369. Make a 4x4 magic square not a pure magic square whose magic sum is 38. The commonly used methods of constructing magic squares are the cross diagonals method for doubly even. The normal variations of these puzzles in other words, 4x4 puzzles that contain only 116 in their cells. For example, for a 3x3 magic square we say it is an order 3 magic square. It uses the numbers 1 to 16 inclusive, and its magic total is 34, as predicted by the formula shown on another page. We will find the generalized form of a 4 x 4 magic square with help of 4 x 4. In a magic square, the numbers in each row, column, and diagonal. We hope that you find exactly what you need for your home or classroom.

In the albrecht durer magic square enlarged to the. But if you are asked to build a magic square with a common sum of 678, you see 678 34 644, and 644 4 161, so you add 161 to every number in the basic magic square and so build a magic square using the integers 162 through 177. Magic squares have been used for centuries and this all around the world. The 4x4 magic square puzzles is solved by finding the values that make the sums all rows, columns and diagonals equal to the same value. And then you divide 20 by 4 to get 5 with no remainder. The magic sum of each of the order3 squares form an order 4 pandiagonal magic square with the magic sum 870. We will find the generalized form of a 4 x 4 magic square with help of 4. Attempts to provide complete listings of magic squares go back to at least 1693 when frenicle in france concluded there were 880 squares of order 4. Because its square, these values for a given puzzle are the same. Each number can be used no more than two times in each magic square. Having one of the forms of a 4 x 4 magic square, we can proceed to work out larger squares of the form42k. Some literary work magic squares have turned up throughout history, some in the lo shu square. The 4 x 4 magic square to the left is the basic 4 x 4 magic square.

In a magic square all the rows, columns and diagonals add up to the same number. Take a business card and write this 4x4 magic square on the back. A 4x4 magic square is a square of 16 distinct integers, where the sum of the entries in all rows, columns and both diagonals is constant. Pdf on jan 20, 2016, bhavya gupta and others published generalized form of a 4x4 magic square find, read and cite all the research you. The lo shu square is an ancient 3x3 a mathematical context. This method does not use mathematical formula in the construction of the magic square. For example, if x 2, y 5 and v 8, the resulting square will be as shown in fig. Pdf generalized form of a 4x4 magic square bhavya gupta. The order for a magic square dimension of the horizontal and vertical axis of the square.