Mathturion

Reversing the Train

Eight cars begin in order: 1, 2, 3, 4, 5, 6, 7 on the main line, with 8 alone beyond the right-handtopmost switch. The locomotive starts parked on the passing track.

Your goal is to rearrange the cars so they appear in reverse order on the main line:

8, 7, 6, 5, 4, 3, 2, 1

The locomotive must finish parked on the passing track again.

This is an old shop-sign puzzle. Customers were challenged to solve it in 20 moves, but the true minimum is 26.

The track has two connected parts: a main line with nine slots and a passing track with five slots. Each slot can hold only one car or the locomotive. The two switches connect the ends of the main line to the ends of the passing track.

Cars and the locomotive can slide along a clear track into an empty slot. Sliding along the same track is free. Each time a piece crosses a switch between the main line and the passing track, it counts as one move.

Drag any car or the locomotive to an empty slot. It will snap into place if the move is legal; otherwise, it returns to where it started. To move a piece between the two tracks, drag it across a switch — each crossing counts as one move.