Fundamentals of Game Design: Math & Art

Fundamentals of Game Design: Math & Art

In order to produce interactive worlds that engage users through problem-solving, game design must draw from the fields of computer science/programming, creative writing, and graphic design. It is at the junction of math and art that this form of play can be constructed. Professor and Director of Film & Media Studies and Professor of Computer Science & Engineering, Ian Bogost, is an award-winning game designer. In a presentation where he explores the theory and concepts of play and games, he shares that play is paradoxical. Play produces a feeling of freedom through the reducing, rather than expanding, of opportunities. This is devised through the implementation of constraints and limitations. He explains this core theory, at the root of all game design, with the nine dot puzzle. 

Nine Dot Puzzle

The problem is to connect the dots with no more than 4 straight lines without lifting your hand from the paper. Initially, the puzzle seems impossible to solve without the use of at least 5 straight lines. 

Nine Dot Puzzle Incorrect Solution

However, once you think outside the box and venture out beyond the square boundary of the puzzle, the solution is made clear. 

Nine Dot Puzzle Solved

This exemplifies the paradox because in reducing the options, such as limiting the solution to four lines and prohibiting the lifting of the pencil, the game becomes more interesting. This puzzle also exhibits how math and art interact at the most basic level of game design. Although the puzzle is initially approached as a calculated math problem, it isn’t until it’s interpreted through a more creative lens that it can finally be solved.



Works Cited

Danek, Amory & Wiley, Jennifer & Öllinger, Michael. (2016). Solving Classical Insight 

Problems Without Aha! Experience: 9 Dot, 8 Coin, and Matchstick Arithmetic Problems. The Journal of Problem Solving. 9. 10.7771/1932-6246.1183. 

Enn, Yong. (2022). Game Design Framework. 

Lankoski, Petri (2018): Game Design Research: An Introduction to Theory & Practice. Carnegie 

Mellon University. Journal contribution. https://doi.org/10.1184/R1/6686750.v1 

Lankoski, Petri & Holopainen, Jussi. (2017). Game Design Research: An Overview. 

Washington University Alumni Association. “Think Inside the Box - Power of Arts & Sciences 

Week.” YouTube, 6 Dec. 2021, https://www.youtube.com/watch?v=CapAWl7NMBI.


Images

Gerstner, Nicholas. (2022). Thinking With(in) the Box: The nine dot puzzle. 10.22215/stkt/gn61. 

Inie, Nanna & Dalsgaard, Peter. (2017). A Typology of Design Ideas. 393-406. 

10.1145/3059454.3059464. 

Lu, Jackson & Martin, Ashley & Usova, Anastasia & Galinsky, Adam. (2019). Creativity and 

humor across cultures: Where Aha meets Haha. 


Event Screenshot



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