Magic Squares and Polygons
1. (Smallest magic square, 3 x 3)
Using the numbers 1 to 9, fill in the square so that the rows across, down and diagonally all add up to 15.
2. Construct a magic square of 3 x 3 which has a magic constant of 30.
[Hint. Central box must have 30/3 = 10; use the numbers 6 to 14].
3. Using only the numbers 4 through 12, fill in the circles so that the numbers on each straight line add up to 24.
4. Fill in the circles with the numbers from 2 to 6 so that each side of the triangle add up to 10.
5. Fill in the circles with the numbers from 1 to 8 so that each side of the square adds up to 13.
6. (A doubly magic triangle) The numbers 1, 2,...., 9 can be put into circles on the triangle in so many ways that their sum along each side is the same. Can you find an arrangement where sum of the squares along each side are also equal to one another?