Arrow Maze Design Case Study - Part 5 - Regular Arrows

December 7, 2021

Welcome to our next section of topics, Arrow Maze Components. From Part 5 - Part 12 I will look at specific types on blocks that can be used in an Arrow Maze. In this post I start with the most basic arrow, simply called the Regular Arrow.

Here is an overview of what we will be covering in the 14 part series:

Arrow Maze Construction and Design:

Arrow Maze Components:

Part 5 - Regular Arrows

Part 6 - Double Arrows

Extreme Arrow Maze examples:

Arrow Maze Design Case Study - Part 5 - Regular Arrows

The core and most basic element of an arrow maze is the basic arrow, In fact, a beginner Arrow maze can be made using ONLY regular arrows. Let’s look at an example. Here is a 9 x 13 landscape Arrow Maze using only regular arrows. Go ahead and take some time to solve it.

Arrow Maze full of only regular arrows — Regular Arrow Maze

How was the experience ? If you chose the right path from the START it was a quick solve. If you did not chose correctly you eventually found this out when you returned to START after moving around the maze,

A maze with this design (regular arrows with no choices) is virtually the same in structure as a line leads maze popular in kids activity books. Let’s look at one of my Line Leads Mazes:

In both, you make an initial choice of paths, then follow it to see if you are correct. The incorrect Arrow pathways bring you back to START while the Line Leads Maze takes you back to another incorrect possible pathway. Otherwise these are very similar.

Let’s focus in on the START in our example. Highlighted in light blue, there are 4 possible pathways you may move to and one return pathway (which technically can be chosen but will immediately return you back to start). Your chance of choosing the correct path is 25%.

From a design standpoint you might be asking, wait, if there are 4 pathways out and only 1 is correct, leaving 3 incorrect pathways, how is there only 1 pathway back to the start ? Well, all of those incorrect pathways meet in 2 spots to form one incorrect pathway back to START. Again the highlighted section shows what we are speaking about. Incorrect pathways Yellow and Green combine at the Blue arrow which then combines with the 3rd incorrect pathway of Purple at the first Red arrow. The last 3 red arrows represent all 3 pathways (Yellow, Green, Purple) moving back to the START.

Arrow Maze incorrect paths design explanation

And finally, let’s look at each pathway to break down what happened in this maze. Purple, Green, and Yellow are the full false pathways (combining still to red in the end). Black arrows are the correct pathway. Two highlighted black arrows are “filler” arrows that are not actually used in any solution !!!

Arrow Maze with all possible pathways shown

One last design technique you should be aware of when using regular arrows to design a maze. You may or may not have noticed that I usually use arrows at 45 degree angles (did you notice this before ?). I want to explain why this is the case. If you use arrows pointing in the standard NSEW directions, you will create pathways that CANNOT be crossed over. But using 45 degree angles will fix that. In the example below I have drawn one pathway using NSEW arrows and one with 45 degree arrows that travel essentially the same way. But if I continued to design each maze the NSEW version does not have much flexibility on where future pathways can go because the arrows have created a wall that cannot be crossed over.

Arrow Maze Design example - arrow directions

In Part 6 I will discuss the Double Arrow

Arrow Maze Design Case Study - Part 4 - Using Loops

December 5, 2021

Welcome to Part 4 of our Arrow Maze Design Case study where we will look at the use of loops. Loops are a great way to have some fun with the solver and create an interesting maze. They also allow the maze designer to help a solver move towards the goal without moving backwards. This is the last topic in the maze construction section.

Here is an overview of what we will be covering in the 14 part series:

Arrow Maze Construction and Design:

Arrow Maze Components:

Part 5 - Regular Arrows

Part 6 - Double Arrows

Extreme Arrow Maze examples:

Arrow Maze Design Case Study - Part 4 - Using Loops

For this example I will use a 9x9 box Arrow Maze, and fill it with a lot of intersections (and make those into loops). We already discussed in Part 3 how the more intersections that are used, the more difficult the maze becomes. This example has 9 intersections. Take some time and try to solve it.

What did you think ? Did you notice the loops in the maze ? I assume yes. I took some time to highlight the loops throughout the maze. First notice that I have a constructed START (we will speak about this in a future post). No matter which of the 3 blocks you move to from the START they all lead to the first intersection.

Now let’s follow the loops. RED is first. If you take the red path it leads back to where you are OR leads you to the next loop PURPLE which then leads you back to the RED loop either way !

The next pathway is the BLUE loop, which takes you to another intersection ( the blue double arrow) which takes you back into the RED / PURPLE loop or into the GREEN loop that circles back to the BLUE intersection -> to the RED PURPLE… UGH, unless you correctly chose the down black direction.

This goes to the BRIGHT GREEN loop that leads back to the first intersection if you take it.

Next is PINK which leads to either BRIGHT GREEN or YELLOW that loops you back to BLUE.

If you take the correct pathway from PINK you have only one loop remaining, the simple GREY that loops onto itself.

Loops, and loops within loops are a great way to make the maze interesting for the solver. Use them liberally and you will not need to send the solver back to the START. If you are designing a arrow maze for kids, loops are extremely important. I consider short loops the same as short, obvious dead ends in a regular maze…if you take it, you can quickly get back on track and moving towards the goal.

In Part 5 we start our topics on the individual components of the Arrow maze with the most basic component - Regular arrows,

Arrow Maze Design Case Study - Part 3 - Intersections

December 2, 2021

Welcome to Part 3 of our Arrow Maze Design Case study. We will look at the use of Intersection Arrows. Of all the arrows used these are the key arrows that create choice in an Arrow maze. Without them an Arrow maze would be more like an Arrow labyrinth.

Here is an overview of what we will be covering in the 14 part series:

Arrow Maze Construction and Design:

Arrow Maze Components:

Part 5 - Regular Arrows

Part 6 - Double Arrows

Extreme Arrow Maze examples:

Arrow Maze Design Case Study - Part 3- Intersections

For our first example we will use a 9 x 13 landscape Arrow Maze, and fill it with a total of 13 L shaped Intersections. These intersections are the standard way in an arrow maze to give the solver a decision to make on what direction they would like to continue in. The more choices (intersections) the more difficult the maze, since only one pathway will lead to the GOAL.

One of the great ways to use these intersection arrows is next to the START block, which will naturally expand the initial options of the solver. As shown in RED below, the 4 starting moves actually work like 6 possible starting moves/paths to choose since 2 intersections are possible from the START. If you are starting an Arrow maze from a tight space (say a corner), consider adding intersections right off the bat !

Arrow Maze possible starting moves shown

While this Arrow Maze used only L shaped intersections, you can also have an opposite direction decision arrow that works in the same way. Here is an example from my book (page 39). Take some time and try to solve this one. I used an extensive Looping system while constructing it that is intended to send the solver back near the start multiple times (unless you are lucky !!). It is actually a good example of that construction that we will cover in a future post.

This 8x9 Arrow Maze contains 70 solving blocks (72 minus START and GOAL) and 13 decisions, or roughly one every 18.5% of blocks (vs my first example 13/115 =11% of blocks). So despite being a smaller maze by 37% you are much more likely to get lost in it (in theory).

The summary of intersections - the more you use the more difficult the arrow maze.

In Part 4 I will look at the use of loops in a maze construction, a must for any arrow maze designer !

Arrow Maze Design Case Study - Part 2 Using Creative Shapes

November 30, 2021

Welcome to Part 2 of our Arrow Maze Design Case study. In this section of the case study we will look at the shape of the overall arrow maze. I call it using creative shapes, but it can just as easily be simple shapes.

Here is an overview of what we will be covering in the 14 part series:

Arrow Maze Construction and Design:

Arrow Maze Components:

Part 5 - Regular Arrows

Part 6 - Double Arrows

Extreme Arrow Maze examples:

Arrow Maze Design Case Study - Part 2 - Using Creative Shapes

The shape and size of the Arrow Maze will help determine the difficulty level and funability which is apparently not a word. Well, I say it is.

Funability - a measure how much fun an event or item contains

Now that we have that out of the way let’s begin with some obvious statements.

The larger the Arrow Maze (as measured by the number of blocks) the more difficult the potential maze
Interesting shapes, including those with notches and gaps creates a more interesting solving experience and allows for more ‘visually hidden’ moves.

Let’s look at a few examples: Simple 9x9 maze (81 blocks). Nothing to write home about. The maze complexity in completely dependent on how the blocks are filled.

Here is a shape that is based off an 8x8 but has cutouts that give it a pinch point in the center. This means the loops do not return you to start, but return you to the midpoint intersection block. The shape essentially splits the maze into two sections.

Based off on an 8 x 9 grid, this maze has a cutout to give it an O shape. In this maze the flow of the pathways is counterclockwise around the center space.

My next example uses floating blocks that can only be reached by using double arrows. It also includes lots of gaps that can be jumped. Overall the shape helps make a more interesting solve. It includes a forced START move and a double move is needed to reach the GOAL.

I have made a few dozen 45 degree angle Arrow Mazes. This particular maze comes from my maze book (page 49!). While this maze looks interesting and is a nice change of pace from a regular shaped maze, the actual maze design is not really affected. Everything is at a 45 degree angle. I like to mix these in for a change of pace. The shape, however, does have many nocks and crannies to move in and out of !

And let’s look at 3 more shapes that are large scale landscape mazes that I made with interesting shapes to force certain moves. I like all three. Take some time to solve them, I think they are enjoyable mazes.

The moral of this portion of the case study - Be creative with your shapes !

Our next topic in Part 3 - Intersections