Traffic Jam / Let Me Through

Shafir Games 1981.
(cardboard cover, plastic tray, and 10 plastic pieces, 4.8 by 4 by 3/8 inches)

Uses 1x1, 1x2, 2x1, and 2x2 pieces on a 4x5 board in the theme of Dad's Puzzler and Red Donkey. This puzzle is described in Hordern's book (puzzle C28); it is also shown in Figure 1 of a 1990 patent of T. Monoyios. From the start position shown on the left, slide pieces (without picking them up) to form the end position shown on the right:
Here are the directions from the back of the box:


A Traffic Jam Solution Idea
The basic steps for one approach to solve Traffic Jam are shown below, although there are many shorter solutions (the following page shows a minimal length solution).


A Minimal Length Traffic Jam Solution
Here is a solution of 69 straight-line moves; it can be converted to 61 rectilinear moves by combining steps 4/5/6 to 2 moves (rename 243 to 324) and combining steps 2/3, 12/13, 20/21, 26/27, 29/30, 53/54, and 62/63 (89 unit moves are used, although 87 unit moves are possible):


(one move = slide one piece any number of units in one direction)

Traffic Jam Variations
It is natural to consider the simpler puzzle where we only care about the 2x2:


Simple Traffic Jam

Fewer moves are required if starting from the final position of Traffic Jam::


Reverse Simple Traffic Jam

Here is a 39 straight-line moves solution; it can be converted to to 34 rectilinear moves by combining steps 7/8, 16/17, 25/26, 28/29, 30/31:


(one move = slide one piece any number of units in one direction)

Further Reading
Monoyios Patent, from: www.uspto.gov - patent no. 4,927,150
Ling Design Patent, from: www.uspto.gov - patent no. 450,356