This project contains a number of solutions for the magic hexagon puzzle in Forth. The puzzle has been described by minforth as follows:
Place the integers 1..19 in the following Magic Hexagon of rank 3
__A_B_C__
_D_E_F_G_
H_I_J_K_L
_M_N_O_P_
__Q_R_S__
so that the sum of all numbers in a straight line (horizontal and diagonal)
is equal to 38.
Some postings by Anton Ertl about his programs and about performance comparisons of his and Ahmed Melahi's programs. These postings also contain command lines for invoking most of the programs below.
A program that attacks the problem directly, setting each variable to a possible value, and then explicitly checking the constraints for which all variables are now set. The constraints eliminate rotated and mirrored solutions, leaving only one solution, but the program explores the whole search space to prove that the solution is unique. There is code that terminates after finding one solution, but it is commented out.
A variant of ertl-simple.4th where the constraints that suppress
rotated and mirrored solutions are commented out, resulting in twelve
solutions.
A program by Anton Ertl that first builds a semi-general framework for dealing with constraint satisfaction problems, and then uses it to solve the problem. Does not suppress rotated and mirrored solutions, and explores the whole search space.
The last several (mostly relatively hard) bug fixes before the program worked each have their own commit (but they are polluted by debugging scaffolding).
A program by Ahmed Melahi. Stops after the first solution.
An improved program by Ahmed Melahi. Stops after the first solution, but you can comment that part out. Does not contain code for suppressing rotated and mirrored solutions.
An optimized variant of `melahi2.4th' by Ahmed Melahi.
A program by minforth that first generates a permutation before testing any part of it. Marcel Hendrix estimated that this program takes 120000h to find a solution.