Magic Star Examples-2

Order-12A

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.
It's points contain the numbers from 1 to 12.
Its complement is # 826112,  the last basic solution in the list, and obviously has the numbers 13 to 24 at the points.

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).

Order-12C

Index # 325,000 of estimated 800,000+ basic solutions. Each line sums to 50.

This pattern contains four super-imposed triangles
(12 = 4 x 3). Their points sum to 30, 32, 34, 36.

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.

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Order-13A

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.

Order-13B

This is index #10 of more then 3,000,000 basic solutions for order-13B.

Order-13C

This is index #10 of more then 3,000,000 basic solutions for order-13C.

Order-13D

This is index #10 of more then 3,000,000 basic solutions for order-13D.

Order-13E

This is index #10 of more then 3,000,000 basic solutions for order-13E.

Order-14A

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

Pattern 14B is continuous.

This is index #10 of more then 7,000,000? basic solutions for order-14B.

Order-14C

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

This is index #2215000 of more then 7,000,000? basic solutions for order-14D.

Total number of solutions
The numbers given for estimates of the number of basic solutions is just that, an estimate. Because of the large number of solutions, it is impossible to find them all in a reasonable time span. However, time required varies directly with the number of consecutively names points in the pattern. This pattern, with only 2 consecutive point names (AA and BB), runs thousands of times faster then, say, order-14 patterns A, C and E with their 7 consecutive point names.
I started this run on Dec. 24/00 and by Feb. 10/01 had reached solution # 2,215,000. The first number in the solution (cell A) is still 1 and the 2nd number (cell B) now 14. Solution lists for the smaller orders indicate that when the first number becomes a two, approximately one half the solutions have been found.

Order-14E

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.