This page contains examples of magic stars from order-12 to order-14. 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 | Order-12a ....# 275 of > 800,000 | Order-12b ....# 397829 of > 800,000 |
Order-12c ....# 325000 of > 800,000 | Order-12d ....# 277030 of > 800,000 | Order-13a ....# 10 of > 3,000,000 |
Order-13b ....# 10 of > 3,000,000 | Order-13c ....# 10 of > 3,000,000 | Order-13d ....# 10 of > 3,000,000 |
Order-13e ....# 10 of > 3,000,000 | Order-14a ....# 10 of > 7,000,000? | Order-14b ....# 10 of > 7,000,000? |
Order-14c ....# 10 of > 7,000,000? | Order-14d ....# 10 of > 7,000,000? | Order-14e ....# 10 of > 7,000,000? |
Order-12A |
Order-12 uses the consecutive numbers from 1 to 24 (2 x 12). Patterns A, B and C are non-continuous, pattern D is continuous. Index # 475? of estimated 800,000+ basic solutions. Each line sums to 50. This pattern contains two super-imposed 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. |
Order-12B |
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 super-imposed squares (12 = 3 x 4).
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Order-12C |
Index # 325,000 of estimated 800,000+ basic solutions. Each line sums to 50. This pattern contains four super-imposed triangles
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Order-12D |
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
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Order-13A
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Order-13 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 order-13A.
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Order-13B
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This is index #10 of more then 3,000,000 basic solutions for order-13B.
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Order-13C
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This is index #10 of more then 3,000,000 basic solutions for order-13C.
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Order-13D
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This is index #10 of more then 3,000,000 basic solutions for order-13D.
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Order-13E
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This is index #10 of more then 3,000,000 basic solutions for order-13E.
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Order-14A
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Order-14 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 non-continuous, the other 2 are continuous. Pattern 14A is non-continuous. 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 order-14A. |
Order-14B
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Pattern 14B is continuous. This is index #10 of more then 7,000,000? basic solutions for order-14B.
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Order-14C
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Pattern 14C is non-continuous. 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 order-14C. |
Order-14D
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Pattern 14D is a continuous pattern. This is index #2215000 of more then 7,000,000? basic solutions for order-14D. Total number of solutions |
Order-14E
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Pattern 14E is non-continuous. 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 order-14E.
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Harvey Heinz harveyheinz@shaw.ca
Last updated March 01, 2005
Copyright © 2001 by Harvey D. Heinz