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Extended Knight's Tour (Posted on 2008-07-10) Difficulty: 4 of 5
Our valiant knight is about to embark on a longer tour than usual, but he doesn't mind, because there is a lovely young maid waiting at his destination.

The Knight enters the upper chess board at number 1, visiting each cell, just once, in numerical order. When he reaches number 64, he makes another Knight's Move to number 65 in the lower board. He then proceeds in the same manner until he reaches his destination at number 128.

Can you recreate the tour?
               
               
               
               
          6    
               
               
               
               
               
      128        
               
               
               
               
               
KEY:
Blue = cube numbers (1, 8, 27,64 and 125)
Green = squares which are not cubes (4, 9, 16, 25, 36, 49, 81, 100 and 121)
Red = prime numbers (2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31, 37, 41, 43, 47, 53, 59, 61, 67, 71, 73, 79, 83, 89, 97, 101, 103, 107, 109, 113 and 127)
Yellow = multiples of ten which are not square (10, 20, 30, 40, 50, 60, 70, 80, 90, 110 and 120)
Purple = multiples of 11 not included in any other category (22, 33, 44, 55, 66, 77, 88 and 99)
Gold = multiples of 17 greater than 60 (68, 85, 102 and 119)
Rose = multiples of 19 greater than 60 (76, 95 and 114)

Please refer to the above list of numbers for those which occur in more than one category.
Thanks again to Brianjn for all his help.

No Solution Yet Submitted by Josie Faulkner    
Rating: 4.5000 (4 votes)

Comments: ( Back to comment list | You must be logged in to post comments.)
re: Reply | Comment 4 of 7 |
(In reply to Reply by Josie Faulkner)

I was able to use techniques like that for much of the time, but there were a few times (like with 126 connecting to where now is 73 and 107) where I couldn't make any progress other than to reason "well it would have to go here, and then here". In that part, most of the cells that were left were red, and since the prime numbers only come in small chunks, I could figure what went there.

I know I was able to fill in several of the cells on the bottom and left side using the "well something must go here, and the only possibility is __" technique. Maybe the top will be a little easier now that I have some experience with problems of this type? :)

  Posted by Gamer on 2008-07-13 15:55:28

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