Padlock / Puzzle Lock / Lockout

The Padlock (also called Puzzle Lock or sometimes Lockout) is a very intimidating puzzle. It looks insanely complicated, and it is not immediately clear how it is supposed to work. The main idea is that one person sets a combination and mixes it, and then another person has to unscramble it by matching the combination in order to release the locking mechanism.

This puzzle was patented by Ira Friedman on 8 November 1988, US 4,782,676. Ira Friedman also invented and patented Switchback by Binary Arts (now called ThinkFun).

Terminology:

The padlock consists of a black casing with the following parts:

A grey loop at the top. The aim is obviously to pull the loop out of the puzzle, thus opening the padlock.
Green switches, eleven switches on the left hand side, and the same number on the right. These are used for setting a combination.
Blue tiles. There are nine tiles in a 2 by 5 central playing area of the puzzle, and one blank space so that the tiles can slide about.
Blue sliders. These are horizontal sliders embedded in tracks in the surface of the blue tiles.
Red release switches near the top. These release the lock once the puzzle is solved.

Setting a combination:

To set a combination for someone to solve, you must first open it. For the moment I will assume that all the switches are inactive, i.e. all the green switches are pushed outwards towards the edge. To open the lock, you can then simply shift the tiles so that the blank is in the top row, shift both release switches inwards and remove the loop. If not all switches are inactive, then you will have to solve the puzzle first, and I will describe that later.

Now that the lock is open and the loop removed, you can set up a combination:

Slide the release switches out of the way, and mix up the sliding tiles. Note that it is possible to pull up a tile, rotate its surface 180 degrees, and then push it back in. Continue until you are satisfied that the playing area is well mixed with the blank on the top row again. Note that it is possible to push the whole playing area up and down a bit to align it with the switches in two ways.
Now push as many switches as possible inwards, into the playing area. The switches can be moved into the tracks on the tiles. Any switches that cannot encroach the playing area should be left in the outward inactive position.
Push the release switches inwards.
Carefully insert the loop into the puzzle. It will not go in all the way unless each switch is either inactive or pushed into the playing area.
Push the release switches outwards again.
Push all the 'activated' switches as far outwards as possible. These switches will not go all the way outwards, but will go far enough to release the tiles in the playing area.
Mix the tiles by sliding them around.

Solving a combination:

Another person can then solve by reversing the steps above:

Unscramble the tiles by sliding them around, trying to place them such that all activated switches are given room to slide further inwards, and such that the blank lies in the top row. Remember that the playing area can be shifted up or down as a whole to align with the switches in two ways. It is considered cheating to pull up and reverse a tile to reach a solution, though you may well have to resort to this tactic if it is too difficult.
Slide all activated switches inwards, into the playing area.
Slide the release switches inwards.
Pull out the loop.
Reset all switches, pushing them outwards to the inactive position.
Clean up by reinserting the loop and pushing the release switches outwards.

The number of positions:

It very much depends on what you wish to count as a position. Given a particular orientation of the tiles, then there are 9!/2 = 181,440 ways of arranging the tiles such that the blank is in the top row. The division by 2 is because of the usual parity restriction in sliding tile puzzles.

On the other hand you may want to know how many different combinations it is possible to set. Suppose that when you set the combination you always activate as many switches as possible. In that case the combination depends mostly on the position and orientation of the tiles, so then there are at about 2⁹ * 9! /2 = 92,897,280 possible challenges you can set. This is an inaccurate because sometimes a track contains a long and a short slider and you can activate either switch (but not both). Furthermore, some combinations have several solutions, and those have been counted separately in this calculation.
If you do not restrict yourself to always activating as many switches as possible, then there are at most 2²² switch settings and 2⁹ tile orientations to give at most 2³¹ = 2,147,483,648 challenges. Clearly however not all of these are really solvable. For example at most 14 switches can be active at any one time (the tiles have 15 gaps and at least one is in the tile in the top row and so cannot be used).

Hints for solving:

There is no straightforward method for solving the padlock, but here are a few hints that may simplify things a little.

Shift the playing area to the up or down position, and keep it there throughout. Only if you find that you cannot solve it slide it to the other position and try again.
Start from the bottom row, and solve your way upwards row by row. This leaves the blank and the unused piece at the top at the end.
As you solve each tile row, ensure that each activated switch can be moved. In fact, you may as well move them inwards before you move up to the next row, so that you are less likely to accidentally disturb previously solved tiles later on.
There are only 15 track gaps on the tiles, which are needed for those activated switches. You must use up as few of them as possible on each row, leaving more for solving the later rows.
Sometimes it is possible to work out beforehand if the playing area should be shifted up or down. Count how many track gaps there are on the bottom tracks of the tiles, how many on the middle tracks (should be 5), and how many on the top tracks. Then find out how many switches those three sets of gaps should each deactivate. If there are not enough gaps to deactivate them all, then you will have to shift the playing area to the other position.
When you are trying to solve the last (top) row, it may happen that the three tiles are in the wrong order, i.e. it could be solved if two of the tiles were swapped. This is not possible without disturbing tiles on the lower rows. See if it is possible to replace any of the previously used tiles with one of the final three, or if two of the previously used tiles could be swapped.

Jaap's Puzzle Page