How do you solve it?

TIPS FOR SOLVING COGISMO PUZZLES

Below are some techniques that are useful in solving Cogismo puzzles.  These may not be the fastest or most efficient techniques, but they should allow you to solve level 1 to 4 Cogismo puzzles.  Don’t worry about this page being a spoiler.  These tips will speed up your learning, but you’ll still need to do the same amount of mental heavy lifting.  That’s a good thing about Cogismo; there is no easy way.

The basics

Understand that there are twenty possible states for each cog.  There are 4 positions that a cog can point in, and 10 numbers that it can display.

Why should you care?  Because this means that:

• you must tap a cog twenty times before it will return to the same state that it started in (assuming that it doesn’t get knocked by another cog); and
• within any instance of the puzzle, for any given cog, even numbers will always have one orientation (either horizontal or vertical) while odd numbers will always have the opposite orientation.  For an example look at the diagram above, and note how the even numbered cogs always point either up or down, and the odd numbered cogs always point left or right.

With that knowledge, start by finding any cogs that can be made to display a zero while pointing only into empty space. Rotate these cogs into their solved position.  Note that, unless you accidentally tap on them again, these cogs are now “safe”.

Next, find any cogs that can be made to display a zero while pointing only into empty space or at an already solved cog. Rotate these into their solved position.

Keep repeating the process of identifying cogs that can be made to display zero while pointing only into empty space or at an already solved cog.

The steps above are enough, on their own, to solve the easiest Cogismo puzzles; but for the medium and hard puzzles you are going to need to do some extra thinking.

The next steps

Determine the required final orientation for all unsolved cogs.  In the example shown below:

• the left hand cog in the 3rd row will need to end the puzzle with a vertical orientation, because it can never be made to display a zero while in a horizontal orientation.
• the left hand cog in the 2nd row will also need to end the puzzle with a vertical orientation (for the same reason); but it won’t be able to end the puzzle orientated down, because the required end position of the cog below it will obstruct that.  So the only orientation in which the left hand cog in the 2nd row can be solved is when its sole tooth is facing up.
• using this type of analysis, the final orientation in which each of the five unsolved cogs will need to end, can be determined. These are shown in yellow below.

Rotate the unsolved cogs so that they are as close as possible to their required final state, and displaying at least a 7, but are still “out of the way” of other cogs.  The “at least a 7” rule is important, because cogs showing lower numbers run the risk of getting stuck behind solved cogs.  In this example, the path to solving the Cogismo puzzle from here is obvious.

Difficulty levels 3 and 4

At this stage you’re probably thinking that Cogismo isn’t challenging enough for you, so lets switch to a new example, with a higher difficulty level.

Note that, in this example, there are no cogs that can be solved using the “find any cogs that can be made to display zero while pointing only into empty space” technique.  We are going to need to go straight to the “determine the required final orientation for all unsolved cogs” technique.  In the case of our new example, there is only one possible solution for the final orientation of the cogs, and this is shown in yellow below.

Then do the “rotate the unsolved cogs so that they are as close as possible to their required final state, and displaying at least a 7, but are still out of the way of other cogs” step.  In this worked example, we can actually solve two of the bottom row cogs in this step.

It is from this point that solving Cogismo puzzles starts to get “interesting”.  We need to think through how the cogs are going to interact, in order to determine the correct sequence of our final few cog taps. In this example the two right hand cogs can now be solved, and the top cogs rotated a little further.

Now we are at the critical junction.  Any cog tap that would cause the middle cog in the top row to rotate before the left cog in the top row rotates, will undo most of our progress to date; because if middle top cog rotates first, then it will initially move into the solved position, but it will also set the left top cog rotating, which will immediately knock the middle top cog out of the solved position.  That would not be good.   Of the five cogs that remain in an unsolved position, four would result in the middle top cog rotating before the left top cog (and the associated yells of frustration).  But if we tap of the left top cog then we are left only two obvious taps from solving the puzzle.

When you are doing the level 4 Cogismo puzzles, the level of interaction between the cogs is often very complex.  You are going to need to “think ahead” and reason through what the correct sequence of cog taps is.   If levels 1 and 2 are just too easy for you, then you should be able to find something that provides you with an adequate level of challenge on the higher levels.

Difficulty level 5

Time for a confession.  We don’t know how to reliably solve difficulty level 5 Cogismo puzzles.  At difficulty level 5, the amount of interaction between the cogs is so complex that it is common for a single cog tap to result in the cogs gaining more than three increments.  Because of this – making base camp with all of your cogs on 7 or higher (as recommended above) just doesn’t work.

So what makes us think that the difficulty level 5 puzzles are solvable?  Because to generate them we (1) start with a solved puzzle then (2) make 18 to 30 random cog presses.  If these puzzles start life solved, surely they can be re-solved. Surely…

If you are looking for the ultimate challenge, then be the first to work out how to RELIABLY solve difficulty level 5 Cogismo puzzles, and let us know.  THIS SPACE IS WAITING FOR YOU.