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Star Trek (Posted on 2005-09-23) Difficulty: 3 of 5
                                    
                  * * * * * 
            * * * * 4 7 7 * * * * 
        * * * 5 4 4 8 3 3 4 6 3 * * * 
      * * 1 4 5 1 1 1 4 5 1 7 1 3 5 * *
    * * 4 9 4 9 6 7 5 5 5 8 7 6 6 8 5 * *
    * 3 7 2 9 8 3 5 6 7 3 9 1 8 7 5 8 5 *
  * * 1 4 7 8 4 2 9 2 7 1 1 8 2 2 7 6 3 * *
  * 7 2 1 8 5 5 3 1 1 3 1 3 3 4 2 8 6 1 3 *
  * 4 2 6 7 2 5 2 4 2 2 5 4 3 2 8 1 7 7 3 *
* * 4 1 6 5 1 1 1 9 1 4 3 4 4 3 1 9 8 2 7 * *
* 4 3 5 2 3 2 2 3 2 4 2 5 3 5 1 1 3 5 5 3 7 *
* 2 7 1 5 1 1 3 1 5 3(3)2 4 2 3 7 7 5 4 2 7 *
* 2 5 2 2 6 1 2 4 4 6 3 4 1 2 1 2 6 5 1 8 8 *
* * 4 3 7 5 1 9 3 4 4 5 2 9 4 1 9 5 7 4 8 * *
  * 4 1 6 7 8 3 4 3 4 1 3 1 2 3 2 3 6 2 4 *
  * 7 3 2 6 1 5 3 9 2 3 2 1 5 7 5 8 9 5 4 *
  * * 1 6 7 3 4 8 1 2 1 2 1 2 2 8 9 4 1 * *
    * 2 5 4 7 8 7 5 6 1 3 5 7 8 7 2 9 3 *
    * * 6 5 6 4 6 7 2 5 2 2 6 3 4 7 4 * *
      * * 2 3 1 2 3 3 3 2 1 3 2 1 1 * *
        * * * 7 4 4 5 7 3 4 4 7 * * *
            * * * * 3 3 4 * * * *
                  * * * * *

Starting from the central cell of this maze (there's a (3) in it), the challenge is to find a path that leads you off the maze, and to a "star" (*).

The number at each cell shows how many steps, in a straight line, you must take. You can travel horizontally, vertically, or diagonally, up or down, left or right.

But! You must reach the first star in the direction you are travelling in an exact number of steps, and not go any further. If you reach a star, and still have some steps "left over", you cannot exit that way.

See The Solution Submitted by pcbouhid    
Rating: 3.6000 (5 votes)

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Solution re(3): computer solution -- longer paths | Comment 18 of 27 |
(In reply to re(2): computer solution -- by Charlie)

Since the exit is at the lower left, biasing the search towards the upper right can be expected to give longer paths at the beginning, as shown below.  However, the algorithm used was such that shorter paths to a given point are preferred to longer ones, so even at the beginning of the search, the first found path is not necessarily the longest with its given bias.

Also, beyond the scope of the algorithm would be to find a path that includes all the nodes in the longest possible path.

But here's a long one with 176 steps (the g7 represents 177, as letters are used to combine two digits, with z0 representing 100; z1, 101; a0, 110; a1, 111; etc.).

                                                                                                         
                                              804    7  247                                             
                                               /           \                                            
                                                                                                        
                                 5    4   74> 998    3 < 63   84    6 < 53                              
                                                v               \                                       
                                                                                                        
                       1    4  195>   1    1    1    4  205>   1 <187    1    3  215                    
                                                                                   v                    
                                                                                                        
                974  779  294    9  476  137> 155> 645  115><768  407  166 <146 <128  g35               
                  v     \    \         \             v               \    \            /                
                                                           /        ^                                   
             3  337>   2  819  678    3  385> 366> 347>  43 <329  391 <668 <377 < 35 <358  495          
                             \    \                                                          v          
                                      ^          /         /                   /                        
             1  894  d87  578    4  462  729> 102 <887  311  551><568    2  g22 < 97  736    3          
                   \   v     \                                                          v               
                                                 /             ^   \                   \                
      z57    2    1  938    5    5 <923  861> 871 <913    1  753  633    4 <622 <858  236    1  e63     
         \              \                                                                         v     
         /         /                  ^          /    /              /              /                   
      284    2  986  c37  z22 <275  452  a04> 302  542 <265  a14   23  e42 <448  221  a87 <257    3     
                        \  /                                    \         \            /                
                           \                   \      /                       ^        \                
        4    1    6    5  c21    1  a41> a59  z91  654    3  g44 <z84    3  431  b29  798    2    7     
                                            \                 /                    v                    
        ^                   ^          /    /                   /    /         /    /                 \ 
   4  z43    5 <z32  c73  z12 <c62  903  532 <z04  c92    5  613  485    1  b11  e53 <605  505  e73  177
                        \                             \                                      v    v     
                                           ^          /    /    /    /   ^                              
   2    7    1  b75  d61 <d51 <b63    1  715 <b53   13  z72  844  422  e33 <707 <b47 <835    4    2 <417
                   \   v                                                                                
                       ^    ^                    /  \                /    /    /       \                
   2    5    2  d32> d76  d41    2 <d24  f24  g16  a33 <d14 <d01  b02  691  592 <a26  745    1    8    8
                                            \                                                           
                                       /       \              \      /   ^                              
 g70    4    3    7  d95    1    9  c83  g54  c14    5 <c02  969  784  681    9    5    7    4  e88     
                        \                 /                                                      /      
                                            /              /   ^     /    /             ^               
        4    1    6    7    8    3  f94  z63    4    1  e23  951  582  823  f52    3  a76    2    4     
                                     /                                         \                        
                                                 /    /        ^   \                                    
        7    3    2    6    1    5    3    9  b92  a93  c42  941  525    7    5    8    9 <515    4     
                                                           \                                            
                                            /  \          ^          /                                  
             1    6    7    3    4    8  b81  f82    1  e12  f31> f42    2    8    9  f64    1          
                                                                                       /                
                      \                    ^                       \                                    
             2    5  g64    7    8    7  f15    6    1    3    5  c57    8 <f07    2    9    3          
                                                                                                        
                   /                             /                                 ^    ^               
                g06    5    6    4    6    7  e02    5    2    2    6    3    4  b37  a64               
                                                                                                        
                                                                                                        
                       2    3    1    2    3    3    3    2    1    3    2    1    1                    
                                                                                                        
                                                                   \                                    
                                 7    4    4    5    7    3    4  f74    7                              
                                                                                                        
                                                           /                                            
                                                3    3  e94                                             

  Posted by Charlie on 2005-09-24 19:16:50
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