Interactive puzzle that is engaging. It gives pupils the opportunity to solve a problem that requires flexible thinking. The problem is simple. Numbers form 1 to 9 is used, but each number is used only once. The goal to achieve is the sum of each row and column, and diagonally, should be 15. There are four different ways to achieve that.
Note: for 3 x3 magic square
1 + 2 + 3 + 4 + 5 + 6 + 7 + 8 + 9 = 45
45 /3 = 15 ( 3 rows or columns share the 45)
For 5 x 5 magic square the sum of each row, column or diagonal is 65.
For 7 x 7 the sum is 175.
The rule:
- Enter 1 in the middle of the first row.
- Go through right corner (small arrow line through the corner will help).
- Once outside the boundary of the main square fill the next number at end of that row or column.
- Keep on going through right corner and if you find empty square fill the next number there, but if you find it is already occupied, fill the next number in the square immediately below.
Exception: since there there is no row or column after filling top right corner square, fill the next number in the square immediately under it.
The general formula for the row sum is:
Last x (Last + 1) /( 2*R) where R = Number of rows
Example, for 3 x 3 magic square (9 x 10 )/(2 x 3) =15
for 5 x 5 magic square (25 x 26)/(2 x 5) = 65
for 7 x 7 magic square (49 x 50)/(2 x 7) = 175
Hint: One could use the 5 x 5 and 7 x7 magic squares to practice mental arithmetic, using the idea of number bonds.
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