* 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