A knight enters the grid at number 1 and then moves, as if he were on a chessboard, to number 2. He visits every square in numerical order, before exiting at number 64.

KEY:
Blue = cube numbers (1, 8, 27 and 64)
Green = squares which are not cubes (4, 9, 16, 25, 36 and 49)
Red = prime numbers (2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31, 37, 41, 43, 47, 53, 59 and 61)
Yellow = multiples of ten (10, 20, 30, 40, 50 and 60)
Purple = multiples of 11 which are not prime (22, 33, 44 and 55)

One number has been added to get you started.

				35

(In reply to re: computer solution by Charlie)

The only way you'd manage a background would be to place the array within a one cell table, and I doubt if any of us have a sanction for that in comments, although editing with View Source, while messy, might work.  (??)

<table><tr><td bgcolor="#000000">

  1 16 31 40  3 18 21 64
   30 39  2 17 42 63  4 19
   15 32 41 46 53 20 61 22
   38 29 48 43 62 45 54  5
   33 14 37 52 47 58 23 60
   28 49 34 57 44 55  6  9
   13 36 51 26 11  8 59 24
   50 27 12 35 56 25 10  7
  

</td></tr></table>

With view source I created the HTML tags as shown, and pasted Charlie's code from the Page source, from and including the Pre tags.  Something else beyond us.

Edited on January 24, 2008, 7:29 pm

Posted by brianjn on 2008-01-24 19:03:45