This page contains examples of magic stars from order12 to order14. Because there are multiple patterns for each order there are a total of 14 different magic star examples.
The Magic Star Examples page shows the 14 patterns for orders 5 to 11.
Introduction. . to magic stars  Order12a ....# 275 of > 800,000  Order12b ....# 397829 of > 800,000 
Order12c ....# 325000 of > 800,000  Order12d ....# 277030 of > 800,000  Order13a ....# 10 of > 3,000,000 
Order13b ....# 10 of > 3,000,000  Order13c ....# 10 of > 3,000,000  Order13d ....# 10 of > 3,000,000 
Order13e ....# 10 of > 3,000,000  Order14a ....# 10 of > 7,000,000?  Order14b ....# 10 of > 7,000,000? 
Order14c ....# 10 of > 7,000,000?  Order14d ....# 10 of > 7,000,000?  Order14e ....# 10 of > 7,000,000? 
Order12A 
Order12 uses the consecutive numbers from 1 to 24 (2 x 12). Patterns A, B and C are noncontinuous, pattern D is continuous. Index # 475? of estimated 800,000+ basic solutions. Each line sums to 50. This pattern contains two superimposed hexagons (12 = 2 x 6). In this case the corners of each hexagon sum to 60. In all cases the corners of the two hexagons will sum to the same value. 
Order12B 
Index # 397829 of 826112 basic solutions. My 200 Mhz Pentium Pro, with 64 Megs of RAM took 39.5 days to find the 826112 basic solutions. The data file size is 50 Megabytes. This pattern contains three superimposed squares (12 = 3 x 4).

Order12C 
Index # 325,000 of estimated 800,000+ basic solutions. Each line sums to 50. This pattern contains four superimposed triangles

Order12D 
Index # 277030 of estimated 800,000+ basic solutions. Each line sums to 50. This pattern is the only one of four for this order that is continuous. I

Order13A

Order13 uses the numbers from 1 to 26. Each of the 13 lines sums to 54. There are five different patterns in this order and because 13 is a prime number, all 5 patterns are continuous. This is index #10 of more then 3,000,000 basic solutions for order13A.

Order13B

This is index #10 of more then 3,000,000 basic solutions for order13B.

Order13C

This is index #10 of more then 3,000,000 basic solutions for order13C.

Order13D

This is index #10 of more then 3,000,000 basic solutions for order13D.

Order13E

This is index #10 of more then 3,000,000 basic solutions for order13E.

Order14A

Order14 uses the numbers from 1 to 28. Each of the 14 lines sums to 58. There are five different patterns in this order. 3 of the patterns are noncontinuous, the other 2 are continuous. Pattern 14A is noncontinuous. It contains 2 septagons with the points of each summing to the same value. This is index #10 of more then 7,000,000? basic solutions for order14A. 
Order14B

Pattern 14B is continuous. This is index #10 of more then 7,000,000? basic solutions for order14B.

Order14C

Pattern 14C is noncontinuous. It consists of 2 type 7A stars with the points of each summing to the same value. This is index #10 of more then 7,000,000? basic solutions for order14C. 
Order14D

Pattern 14D is a continuous pattern. This is index #2215000 of more then 7,000,000? basic solutions for order14D. Total number of solutions 
Order14E

Pattern 14E is noncontinuous. It consists of 2 type 7B stars with the points of each summing to the same value. This is index #10 of more then 7,000,000? basic solutions for order14E.

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Harvey Heinz harveyheinz@shaw.ca
Last updated March 01, 2005
Copyright © 2001 by Harvey D. Heinz