*Can puzzle complexity serve a transformational goal?*

In this article I will consider this question, by first describing the design process used to create puzzle complexity which serves a transformational goal. Next I will contemplate the results of that puzzle complexity which is contained in the game my team created.

# Introduction

Whilst working towards my Masters of Entertainment Technology at Carnegie Mellon’s Entertainment Technology Center I had the pleasure of working on Angle Jungle.

Angle Jungle is an educational puzzle game for fourth to sixth graders studying geometry. Initially our requirements were up in the air, though we eventually settled on the following rather vague objectives:

- Create an experience involving angles
- Integrate protractor tool usage

# Design

Our ideation process began with brainstorming based on the objectives of our project.

We then went through two iterations of paper prototypes based on our ideas.

From our paper prototypes, we choose to refine two based on feedback.

We parallel we began the process of creating digital prototypes based off these paper prototypes.

Our breakthrough moment came when Jesse Schell, our Professor, posed to us that though these games used angles, both could be played without **thinking** about angles. We therefore needed to make angles **essential** to the experience. This priceless notion lead us to create Angle Jungle’s progenitor, which we called Treasure Hunter.

Treasure Hunter we believed embodied a system where angles were **essential**. At its heart a mechanic that encoded the relationship between the numeric, and spatial representation of angles.

We then began refining Treasure Hunter.

After positive feedback from playtesting we next created a digital prototype.

This digital prototype went through multiple iterations.

At this point in the development process we had the beginnings of a game. The game cried out for something more though. It cried out for a greater experience.

## Experience Crafting

How does one go about creating an experience? There are infinite ways, but we began with considering the difficulty curve within our experience.

### Difficulty Curve

The above graph is an abstract difficulty curve which displays a sequence of tense and release cycles of increasing difficulty. This curve would form the underlying foundation of our experience.

### Gameplay Elements

With an idea of what we wanted the experience to look like, next we conceptualized the elements within the greater experience. The inspiration for this process came from a number of sources including the learning materials of our target demographic.

Our aim was essentially to gamify our target demographics learning material through gameplay elements which attempted to capture aspects of the kind of problems they faced in the classroom.

These gameplay elements would form the core components of the experience.

### More Motivation

Whilst conceptualizing our gameplay elements we also considered the possibility that the puzzle may not be intrinsically motivating enough for players. We therefore created two additional supporting motivational factors.

#### Supporting Actor

A gender neutral character than needed assistance (inspired by Jesse Schell’s lens of help). Given the use of characters in educational experiences is fairly common, and that there exists research on the potential beneficial effects for players. We hoped this would augment learning within our experience.

#### Golden Expectations

In addition we created The Cabin. The Cabin would contain our players reward in the form of treasures and trophies. The Cabin would act as motivational element by creating Golden Expectations (expectation of rewards) through the aesthetic use of empty shelves as well as serve as a measure of game progress.

We also recognized the need to space out our rewards for better impact. We therefore arranged rewards into evenly spaced intervals.

### All Together

Together these pieces could further flesh out the difficulty curve of our experience. The peaks of our difficulty curve would now commonly correspond to the introduction of gameplay elements, and the dips, periods of rest at The Cabin.

The experience needed more though. It was a skeleton crying out for substance in the form of puzzles. It cried out for depth, and complexity.

## Complexity Crafting

With a high level view, and the fundamental elements of the experience in mind we went about crafting puzzles, inspired by our source material and gameplay elements.

This process resulted in a jumbled pile of puzzles which though was a good first step, did not fit the experience structure we wanted. We therefore turned to a mighty tool.

The spreadsheet.

The spreadsheet consisted of columns of each gameplay element which we incrementally increased to increase puzzle complexity. This tool complemented the design process as we created more puzzles based on these new complexity constraints.

Two additional considerations came to mind during this process:

- Include drops in puzzle complexity when introducing new gameplay elements to allow for more effective tutorials
- Have the majority of learning occur early when complexity is low

The result of this work was a structure of thirty levels which we then playtested.

Although initial playtests were largely positive they revealed two design issues:

- Certain puzzles contributed to a lack of ‘Angle Diversity’ (high occurrence totals of fewer number of angle values in the total experience meant a lesser exposure to different angle values)
- Several puzzles had one gem solutions (solutions which required only one angle gem on more complex levels meant less interaction with different angle values within a puzzle)

Both these issues were detrimental to our goal of building familiarity with the angle system, therefore further puzzle analysis was required. Our analysis was twofold:

**Angle Distribution Analysis**– A spreadsheet of counts of each angle value used throughout the experience**Angle Solution Analysis**– A comparison of solution angles against angle values used

These methods revealed a number of such ‘issue’ levels.

The result of iteratively applying this analysis was that both the complexity and angle diversity was maintained, and improved. This ultimately meant a better attempt at achieving our transformational goal.

## New Objectives

So what objective was our experience serving? Though we began with a vague set of requirements. At the end of the project we ended up with a concrete primary transformational objective, and several secondary transformational objectives.

**Primary Transformation**

Build familiarity with the angle system by having players practice solving puzzles using a mechanic that has an encoded relationship between the numeric and spatial representations of angles.

#### Academic Support

- Robert Siegler – Research on the benefits of learning through encoding
- Sharon Carver –
*‘The actual angle choices at the various levels and the angle meter seemed to work well and COULD promote learning of the concepts and spatial relations of angles, as long as students don’t game the system’*

### Secondary Transformations

In addition to our primary transformational objective we took the opportunity to introduce a number of secondary transformational objectives in manners that were natural extensions of the core experience.

#### Protractor Tool Usage

To solve a puzzle a player had to work out the angle that was required to be made to hit an objective. This provided a natural opportunity to introduce a scaffolding tool, the protractor, a measurement device that’s original purpose was designed to aid in angle measurement.

By making this tool available we built in the protractor in a manner that was of a natural clear benefit to our players. We hoped by doing so to build familiarity, and appreciation of the tool by creating a puzzle environment where it was undoubtedly helpful. Playtesting showed that this strategy ‘seemed’ to work.

Sharon Carver – *‘I especially like the meter that shows the full 360 degrees while the player is working on selecting angles. It would definitely be worth testing the impact’*

#### Anticlockwise/Positive & Clockwise/Negative Angles

Introduce the notion of positive and negative angle values.

#### Anticlockwise/Positive & Clockwise/Negative Angle Addition

Introduce both anticlockwise and clockwise rotation, and angle addition and subtraction.

#### Angles Above 180

Expose students to angles greater than 180 degrees.

## Design Considerations

Whilst exposing students to our core mechanic (an encoding between the numeric and spatial representation of angles) through out the experience, initial levels would allow brute force approaches to be rewarded in order to draw in the player with easy rewards.

Considering the support of such ‘brute force’ (choices made without solid reasoning) approaches, the following criticism was raised:

*What if players are not doing the thinking you want?*

In defense of brute force we responded with a number of counter points.

- Absolute mindless play is rare, so given the numeric angle values are essential, even with a brute force approach players are likely to at least reason about this aspect of the game
- Supporting brute force approaches makes the experience more accessible (we had first graders reach level 22 with help!)
- Brute force approaches are only reasonably satisfying in low complexity puzzles (playtesters who solely practiced this method eventually called the game stupid on more complex puzzles)

Most importantly though, we admitted that when complexity was low players would not have to think ‘much’.

This was **intentional**.

The experience **allowed** it for a deeper purpose.

We intended to combine that brute force motivation together with puzzle complexity as a transformative tool. As puzzle complexity increased we intended that the balance naturally shift to incentivize a ‘logical’ approach (choices made based on solid reasoning) given it is more efficient than a brute force approach.

In addition, we believed the benefit of a slow increase of complexity would naturally create skill appropriate ‘teachable moments’, which could be capitalized on by teachers, as students reached the boundary between brute force and logical. A complexity design of this type I called transformational complexity given the experience it created during gameplay.

# Results

The results of this process we believed created an experience that contained:

- Suitable learning and puzzle complexity curves
- An appropriate pattern of tense and release
- Rewards interspersed appropriately
- An exposure to a wide variety of angle values
- A mechanic where angles were essential (encoded the relationship between spatial and numeric representations of angles)
- Relevant and hopefully effective motivational elements

This combination we believe resulted in:

- An engaging enjoyable experience
- Naturally occurring skill appropriate teachable moments
- An environment fostering collaborative play

The transformational complexity we created can be visually best exemplified by the following diagram (note it dips at times of gameplay element introduction).

Well what did our designs ultimately translate into? Get a glimpse in the following promotional video (I’m happy to share raw footage on request).

# Conclusion

So what conclusions can we take away from this experience. First some classic takeaways:

- Paper prototypes are your friend!
- Ask yourself can I play this game without thinking about the core subject matter? Is the subject matter essential to the experience?
- Consider experience curves from the get go to help structure your experience
- Study your target demographics source material, and use it as an additional source of inspiration in your design process
- When introducing new gameplay elements introduce it in a low complexity environment to make learning easier
- Have the majority of learning occur early when complexity is low
- When designing scaffolding tools try to design them in a manner that is of a natural clear benefit to the experience
- If extending your experience is necessary, do so with natural gameplay elements that can serve transformational goals
- Guess and check is not the enemy of education. In fact I believe the availability of simple strategies can create accessibility to larger demographics

Now **finally** back to our original question.

*How can puzzle complexity serve a transformational goal?*

At present my thoughts are twofold:

- Well designed puzzle complexity can create engaging experiences for players which designers can use to piggyback onto to achieve a transformational goal
- Puzzle complexity with brute force motivation can be combined into a transformative tool to create skill appropriate teachable moments at the boundaries of brute force and logical gameplay strategies