That last post came out garbled. The six correct solutions are:

1 (1 -> 2 -> 3 -> 4), #2 (1 -> 2 -> 4 -> 3), #3 (1 -> 3 -> 2 -> 4), #4 (1 -> 3 -> 4 -> 2), #5 (1 -> 4 -> 2 -> 3), and #6 (1 -> 4 -> 3 -> 2).