How to Make a Math Addition Trail Maze

Today I will share with you how to make a variation on the popular Math maze construction that I call an Addition Trail Maze. While a math maze can use dozens of different calculations to solve it, the addition trail maze uses only one, addition. Let’s define what I mean, then get into the example. First, here is my definition of the 2 types of Math Mazes:

Math Maze - A type of number maze where moving from the Start to the Goal is done by correctly answering math problems to move in the correct direction.

Addition Trail Maze - A type of math maze where you move from Start to Goal by adding numbers along the way (the trail) to hit a specific goal number.

How to Make a Math Addition Trail Maze

Step 1 - Draw the Outline

This maze type is not conducive to outline or shapes so I will use a traditional grid-like pattern to illustrate the creation. The outline I use in the example and the most common is a simple square or rectangle, although it can be made in any gridded shape.

Step 1.5 - Choose the Start and Goal

I like using a START and GOAL within the maze placed inside the grid. I choose opposite side of the structure.

Step 2 - Add pathway walls

Next I add pathways to create trails that will become the framework for possible pathways. This choice will determine what possible outcomes at available to you. Notice that I limit the options with a bottleneck between the 3rd and 4th columns. Although the grid I was working with is not shown, this is a 5x5 grid.

As a creator the next few steps happen as part of the design process, but will not be part of the final maze. They are planning steps to create a workable maze.

Step 3 (Planning step 1) - Break the trails into sections

Create sections (mine are in bubbles) which are options that can be moved to. I labeled them with letters. From the START you have 2 options to move in, into section A or into section B. If you move in direction A you will move through 4 blocks before making another decision. If you move onto B you immediately have another decision to make, D or E. When you make your sections for the first time you will make a mistake or 2. The most common mistake is including a block into a section where it does not belong. For example: If you are in A, you MUST next move to C, but C is not part of A. If you move from B to D you also MUST move to C, but C is also not part of D. C must be independent.

Notice that the bottleneck I mentioned in Step 2 is now labeled F and must be used in any solution.

Step 4 (Planning step 2)- Create a decision tree

I made a decision tree to show the possible pathways that can be taken based on my maze construction. To make this easier to see I did not combine common branches i.e. each branch ends with it’s own FMK sequence instead of one common branch. This tells me that I have 8 possible trails to follow which are:

BEFM, BEFK

BDCGFM, BDCGFK

ACGFM, ACGFK

ACDBEFM, ACDBEFK

Step 5 (Planning Step 3) - Add numbers to the sections

Use the 8 possible solutions we found above and assign values to each letter which will create the 8 numbered solutions. Then convert those numbers into the appropriate section of the maze. If plug these into a spreadsheet I can write some formulas to calculate the possible answers. Here is what I used, and their answers:

I can adjust the numbers of each letter as needed to create different sums.

And here are those letters converted to numbers in the actual maze. I used all small numbers, but that is obviously not necessary:

Step 6 - Delete background items

Clean-up the trail maze and come to a final addition trail maze construction.

Step 7 - Add Directions

Add directions to explain to the solver how they can move through the maze. Because you have already made the solution tree in the planning process, this is the time you pick which solution will be the correct one. Because there are 2 possible solutions for 14 I did not pick that number !

Addition trail maze

Step 8 - Create a Final Solution

Highlight the correct path in the final version of the maze to create the final maze solution (shown here in gold).

Note that the final maze is a 5x5 grid, using 23 of the 25 blocks for possible solutions. Let’s look at an abbreviated example to see how a few changes effect things.

Additional Math Trail Maze Example

Here I am using a 6x6 grid and a different internal wall structure which is much more complicated. Going from 23 blocks to 34 blocks really gives us so many more options. We had 8 possible pathway solutions above, any guess how many solutions this maze will have? Here are the abbreviated steps to give you a sense of what I mean.

Steps 1, 2, and 3 Outline, walls, and section the pathways

I have combined the steps for brevity. The walls I used have more gaps and so this leads to more possible pathways. The number of possible sections in our first example was 9 (as shown by having 9 different letters) and here it is 18.

This can be seen in the decision tree below. I did the pathways for B before A. You see a full tree for B while A is abbreviated using those findings so we have a smaller tree to look at. The M, G and U that are colored on the B side of the tree is repeated for the A side, aligning to the colored m, g, and u. Circles reflect the goal. B has 12 ways to reach the goal, as does A, so 24 possible pathways. So that is our answer, 8 possible solutions become 24 with just a slightly larger maze size!

Here is the spreadsheet I made with possible solutions. With some formulas you can play with the #’s that correspond to each letter and see the possible answers change in real time.

Step 5 Add numbers to the sections

Yes I added some negative numbers into the mix. It adds a nice twist to the possible pathways and solutions. It gives the solver more strategy to use in how they move through the maze.

Steps 6, 7 - Delete guides and add directions

I chose 39 as my solution. But I should mention that choosing the largest number you calculate in your spreadsheet is also fun. The smallest number tends to be easier to solve and I do not suggest you use it unless you use many large negative numbers to hide the solution well. There is also some intelligent design you can use by making some sections look different than they may actually be (e.g. a large number followed by some small negative numbers to even everything out).

So that completes the instruction. I hope you enjoy making your own Math Addition Maze !

Here is an early example I made (still called a Math Maze at the time) I am including so you can practice breaking the maze into sections. Good Luck ! The answer is immediately below.

Let’s see how you did:

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How to Make a Mobile Maze

The 43rd type of maze construction I will “how to” is the Mobile Maze. Like some of our other mazes, most notably, the Kids Maze, this type of maze can look many ways and have many different constructions, but it is still has distinct characteristics to properly execute ! Let’s define what a Mobile maze is then get into the step by step instructions !

Mobile Maze - A Maze designed specifically to be viewed and solved on a mobile device.

HOW TO MAKE A MOBILE MAZE

Step 1 - Choose the Maze construction

This seems like an odd Step 1, but it is correct. Similar to a Kids Maze, the Mobile Maze can be created dozens of different ways. Take a look at the How To Draw a Maze section and choose the look you prefer. You will actually be following THOSE sets of instructions while following some basic rules to make the maze look good on mobile ! Also note that some objects lend themselves to this maze construction - a giraffe would be good, as would a anything long.

Step 2 - Follow the instructions + add these rules

Follow the instructions of the maze construction you selected while adding these 2 rules:

1. Design the maze vertically using a 9:16 ratio or greater. The 9:16 ratio is the standard size for a mobile screen (you can read more about screen sizes below) . An easy way to think of this is that you want a maze about twice as high as the width. If you want a maze to be scrollable in order to be solved (this adds some difficulty !), try for a larger ratio like 1:4. What do I mean by that ? Well in a scrollable maze a dead end may be off the visible screen - in fact you might even design your maze with this in mind to make it more challenging !

WHAT A 9:16 RATIO LOOKS LIKE

2. Make pathways that are WIDE. This is a vague but important design feature. I find that a bit of testing is needed to get this just right. If you design digitally it can easily be adjusted (and this is for mobile, so I assume that it is) in order to have a maze that can be solved easily. For Grid based mazes (Grid Maze, Color Grid Maze, Arrow Maze, Block Move, etc.) the widest # of blocks I would suggest using is 5.

Let’s look at a few different Mobile Maze examples:

Here is an example of a Mobile Arrow Maze, that is a 5:13 ratio, and because it is an Arrow Maze, no pathway adjustments are needed ! Because the maze is long the solver cannot see the Goal when they start solving it !

And here is an example of a Mobile Grid Maze. Once again I used a 5:13 ratio. Notice how the pathways between grids are much thicker than usual. I more than doubled the normal width.

A Mobile Weaving Maze. 5:23 ratio, and with very wide pathways. I find that this construction needs more length than others to help establish more realistic false pathways. Still, this is a fun maze to make and solve in a mobile format.

And one more for fun. A Mobile Hidden Message Trail Maze. 5:18.

ADDITIONAL MOBILE MAZE EXAMPLES:

I have a section on the site of over 30 mobile mazes, that includes a free downloadable file of each of them (not really a book since the sizing is for mobile phones, and not for printing). And, although it does not have many words, if you prefer to read and solve laberintos en Español, tengo que aqui.

MAZE DESIGN BASED ON SCREEN SIZE:

Computer screen monitors vary in their aspect ratio, but most since 2012 are 16:9 (1.78), although through time they have varied from 1.25 to 1.60. So, yes, you are not imagining things, computers are getting wider. Some of you might even remember when televisions were a 4:3 aspect ratio (1.33) before they became much wider.

Most smartphones also happen to be a 16:9 (in landscape mode or 9:16 in portrait mode) which is convenient when you use landscape mode to watch YouTube or other videos on your phone. But when you are not watching videos, your phone is in portrait mode for just about everything else you use it for. Tablets have large range of ratios with many 4:3 like an old tv and some 16:10. This makes them a bit wider so that books get formatted as a priority over videos (you are reading with your tablet and not watching movies right ?).

So, when I make a maze for this website I am always thinking about how it will look on a large screen and how it will print on a standard size piece of paper (8.5x11) which is a 1.29 ratio. The mazes still look fine on a cellphone screen, but are not entirely solvable in most cases without zooming in to see the pathways more clearly. This means a lot more difficulty in maneuvering to solve a maze.

So when you make a maze those are the screens you might be making them for. And in this case, Mobile mazes you want to design for a 9:16 screen !

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How to Make a Pod Maze

The 42nd type of maze construction is the Pod Maze. This construction came about from a collaboration with a friend, While the final product can look many different ways, the core ‘pod’ idea stays the same. Let’s define what a Pod maze is then get into the step by step instructions ! I have included a free downloadable book of 31 Pod Mazes at the end of the post.

Pod Maze - A Maze with separated sections, called pods, that must be traveled between to solve the maze. The ability to jump between pods is denoted by small arrows in the pathways.

How to Make a Pod Maze

Step 1 - Draw the Background and Pods

The background will determine the shape of the maze. I typically use a black background to match the color of the pathways I will be drawing. Matching these will save you headaches during construction ! The pod placement and shapes are your choice. Make sure you have enough places where it will become possible to move between pods. The spacing is up to you. In a simple maze closer together will be easier.

Design Option - make the background a light color and change it to the final color during the final step ! This allows the pathways to be more easily seen during drawing !

Step 2 - Choose the Start and Goal (optional)

Choose the start, and optionally the goal and place them in the pods. The goal can always be moved later as the maze is constructed !

Step 3 - Start Mazing

I use a standard construction in the actual pods, but many other options would also work. As you move to the edges of a pod, add a small arrow to indicate where a pathway can cross into the next pod. The adjacent pod should have an arrow aligned in the same plane across to indicate the proper movement allowed as in the example below.

Design Option - When drawing the pathways you could stop them at the pod edges OR continue them across the background (these will be invisible when the background matches the pathway color). If you use a light color background during design this will help with the design !!

Step 4 - Keep mazing and finish the maze

Continue to draw pathways until you have finished completing the entire maze.

Step 5 - Create the Solution (optional)

Make a solution to the maze !

Additional Pod Maze Examples

This additional example uses a spiral construction extensively within the maze.

And this second example adds some color to make the maze more interesting. Nice autumnal colors.

In this third example I mix a few different shapes, using triangles and a center circle as pods.

Free Downloadable Pod Maze Book

The Pod Maze Book

A free downloadable book featuring 31 different pod mazes. Mazes come in a variety of shapes and colors. El libro esta disponible en Español tambien !

File Size: 329 KB

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How to Make a Racing Maze

In a series of posts I will show you how to make a maze in a wide variety of design constructions. The 41st type of maze construction is the Racing Maze. While most constructions are about the making of the specific maze, this one is more about the structure of the maze(s). Let’s define what I mean, then get into the example. At the end of the post I have added a free downloadable maze race book featuring 30 printable maze races !

Racing Maze - A Maze made specifically for racing between two people. The winner is the person that reaches the common goal first.

How to Make a Racing Maze

Before getting into the steps let’s talk about some guidelines for a good racing maze.

1. It is contained on one piece of paper (and preferably a large one) .

2. It consists of identical mazes, one on each side of the page which both end at the goal in the center of the paper. An Escape maze is not the best type for a race (though possible) since the multi-goal option is taken away by the common ending.

3. The maze type should be able to be solved with a writing utensil (to prove the solve has been done). So a maze like an arrow maze would not work easily. Block Move and Warp mazes can also be problematic. If you take a wrong warp an eraser will be needed.

4. Consider the difficulty you want for the maze. Something too difficult will lower the tension that a more speedy maze will create.

Step 1 - Draw Half of the Maze

I have crammed multiple steps into this because you can use multiple different types of maze constructions, each with its own steps. The key is the maze is drawn to fit on slightly less than half the page. It should start at the bottom of the page and end it the center of the page. You may notice the large gap in the example below….that’s it !

Step 2 - Copy and Invert the Maze

Copy the maze you have made and paste it on the top of the page inverted so it faces the opposite direction. This will create 2 identical mazes on one sheet of paper, with each one facing a person sitting across from the other. You will most likely need to adjust the original placement as everything gets centered !

Step 3 - Add final touches

In my example I tag the sides with my website and the name of the maze (or type). I do this because Racing always reminds me of race cars and how they are filled with brand logos. I think this would actually look even better with MORE logos.

Step 4 - Create the Solution (optional)

My guess is that based on the small size and multiple solvers, nobody will be needing a solution, but feel free to create one if you believe it will be needed.

So, you made a racing maze, but do you know the rules and options for the race ? I have it covered and you can find all the information HERE !

Free Downloadable Maze Race Book

THE MAZE RACING BOOK

30 pages, 30 Racing mazes

File Size: 365 KB

Features daily mazes from January 2021. Each racing maze is meant to be solved competitively by 2 people starting at the same time. These are mostly easy mazes with a few weaving mazes at the end a bit harder. To learn about race rules To learn about maze racing rules check out this post.

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Step by step instructions on How to Draw over a dozen different Digital Labyrinths.