Create a Six Point Magic Star

There are several methods of determining the numbers in a magic star. As long as the total of each line is the same, you can use any method you like. We chose the following method due to its relative simplicity. Trial and error is generally the hardest method.

Procedure

  1. Select the line total for the star. For the example star shown, the total or sum is 31.
  2. Calculate the total of all numbers in the star.
    (number of points) x (total for star) / 2
    For the example 6 x 31 / 2 = 93
  3. Split the number determined in step 2 into two parts, both parts must be exactly divisible by 3 (not all divisions will work). For the example, 93 is split into 66 and 27.
    66 + 27 = 93
  4. Choose one number (from the two numbers in step 3) for the total of the inner points, the other number is the total for the outer points. For the example, the inner points total 27 and the outer points total 66.
  5. Select a group of numbers (they do not have to be consecutive) that total the sum of the inner points. For the example 2, 3, 4, 5, 6, and 7 which total 27.
  6. Place the selected numbers from step 5 in the inner points, so that opposite numbers all have the same total. For the example:
  7. Add together each pair of connected inner points on the highlighted triangle. Two triangles form the star, one triangle is highlighted by double lines. For the example:
  8. Write the first total in step 7 (for the example 8) and two numbers that total the star total (for the example 31) either side. You must choose numbers not already used for the inner points. However, the numbers you choose can duplicate the sum just found. For the example:
  9. Write the second number chosen in step 8 (for the example 8) then the next total found in step 7 (for the example 12) and whatever number is required to make the star total. For the example:
  10. Write the last number found in step 9 (for the example 11) then the last total found in step 7 (for the example 7) and whatever number is required to make the star total. For the example:
  11. Check that the first and last numbers in the additions of step 10 are the same. These numbers are underlined for easy identification. If the numbers are equal go to step 14, otherwise go to step 12. In the example calculation they are different.
  12. If the last number is greater (more) than the first number add half the difference between the two numbers to the first number. If the last number is smaller (less) than the first number subtract the difference between the two numbers from the first number. In the example the difference is:
    (15 - 13) / 2 = 1
    So 1 is subtracted from the first number, the resulting addition is:
  13. Recalculate the other numbers so the last number of one addition equals the first number in the next addition. The numbers in the middle of the additions (calculated in step 7 and underlined here) are unchanged.
  14. Check that the numbers at the end of the additions (for the example 9, 10, 14, see step 13) are not duplicated and are not one of the stars inner point numbers. If you have a duplicate start again at step 8, otherwise go to step 15.
  15. Place the numbers found in step 14, in the outer points of the double lined triangle.
  16. Repeat from step 7 for the single lined triangle. For the example, the sum of single line connected inner points are: The additions determined from these are:

In order to make it easier to create a star, we have provided an online development star. To aid your off-line calculations, you can remove all the zeros from the online development star and print.