You are given a box with eight holes labelled   A-to-H,   connected by fifteen straight lines in the pattern as shown below:

             A   B
            /│\ /│\
           / │ X │ \
          /  │/ \│  \
         C───D───E───F
          \  │\ /│  /
           \ │ X │ /
            \│/ \│/
             G   H

You are also given eight pegs numbered   1-to-8.



Objective

Place the eight pegs in the holes so that the (absolute) difference between any two numbers connected by any line is greater than one.



Example

In this attempt:

             4   7
            /│\ /│\
           / │ X │ \
          /  │/ \│  \
         8───1───6───2
          \  │\ /│  /
           \ │ X │ /
            \│/ \│/
             3   5

Note that   7   and   6   are connected and have a difference of   1,   so it is   not   a solution.



Task
Produce and show here   one   solution to the puzzle.



Related tasks

   A* search algorithm
   Solve a Holy Knight's tour
   Knight's tour
   N-queens problem
   Solve a Hidato puzzle
   Solve a Holy Knight's tour
   Solve a Hopido puzzle
   Solve a Numbrix puzzle
   4-rings or 4-squares puzzle


See also
No Connection Puzzle (youtube).




with javascript_semantics
constant txt = """
        A   B
       /|\ /|\
      / | X | \
     /  |/ \|  \
    C - D - E - F
     \  |\ /|  /
      \ | X | /
       \|/ \|/
        G   H
"""
--constant links = "CA DA DB DC EA EB ED FB FE GC GD GE HD HE HF"
constant links = {"","","A","ABC","ABD","BE","CDE","DEF"}
 
function solve(sequence s, integer idx, sequence part)
    object res
    integer v, p
    for i=1 to length(s) do
        v = s[i]
        for j=1 to length(links[idx]) do
            p = links[idx][j]-'@'
            if abs(v-part[p])<2 then v=0 exit end if
        end for
        if v then
            if length(s)=1 then return part&v end if
            res = solve(s[1..i-1]&s[i+1..$],idx+1,part&v)
            if sequence(res) then return res end if
        end if
    end for
    return 0
end function
 
printf(1,substitute_all(txt,"ABCDEFGH",solve("12345678",1,"")))
