A nice result, from http://www.ktn.freeuk.com/9f.htm A fiveleaper is a type of generalised knight that makes moves of length 5 units, with coordinates either {0,5} or {3,4}. In Variant Chess, GP Jelliss made the following observation: Since the fiveleaper has four moves at every square of the 8×8 board it follows that in every closed tour the unused moves are also two at every square, and therefore form either a tour (is this possible?) or a pseudotour (i.e. a set of closed circuits). The question of whether such a double tour is possible was in fact answered in the affirmative by Tom Marlow in a letter to me of 17 November 1991." 5-leaper double tour #1 . 5-leaper double tour #2 20 47 62 55 06 21 46 63 . 46 37 60 11 56 49 04 63 31 42 57 50 11 34 29 44 . 39 24 31 52 27 40 23 32 02 59 16 09 52 03 36 17 . 54 15 06 21 34 29 16 13 13 22 39 26 19 14 23 38 . 57 08 03 64 19 36 59 10 54 05 28 45 64 61 56 07 . 26 41 50 45 38 25 42 51 51 48 35 30 43 58 49 10 . 47 28 61 12 55 48 05 62 32 41 24 37 12 33 40 25 . 20 35 30 53 14 07 22 33 01 60 15 08 53 04 27 18 . 01 18 43 58 09 02 17 44 --Ed Pegg Jr