Log in

View Full Version : how do you solve the magic square using 1,2,3,4,5,6,7,8 and 9. The sum of 18.


AmRiTa XX 21
Apr 11, 2012, 10:52 AM
it's a 3x3 magic square and you need to use the numbers 1 to 9 making sure all rows, columns and diagonals add up to 18.

ebaines
Apr 11, 2012, 10:54 AM
Won't work. If you use the numbers 1 through 9 you can get all the rows, columns, and diagonals to add to 15, but not 18 . Now if you could use the numbers 2 through 10 then they could add to 18.

To get the magic square to work for 15 here's a hint: put the middle number (which is 5) in the middle square. Since you know the row, column, and two diagonals that include the middle square must all add to 15, that means you need to pair up numbers 1 & 9, 2 & 8, 3 & 7, and 4 & 6 to make that work. Now it's just a matter of trying each pair in the various spots and see what works.

If you want to cut down on the trial and error then consider how the number 9 must be placed - to be in a row/column/diagonal that adds to 15 it must be paired with either 1&5 or 2&4. Those are the only two combnations that work. Which means that the 9 must be in a square that only is involved with two column/row/diagonals. So it cannot be placed in a corner (since there corner numbers are pair of three rows/columns/dagonals) or the center. Therefore it must be in the mddle of an edge. Continue this line of thinking for numbers 8, 7, and 6 and you will have it pretty much figured out.