Puzzle—Solving Smartphone Puzzle Apps by Mathematical Programming

Abstract

Abstract. This paper considers six logic puzzles (i.e., single player games) that are available as smartphone apps. The six logic puzzles are: Thermometer Puzzles, Kakuro (Cross Sums), Match 22: Color Puzzle Game, ∞ Infinity Loop, Slider, and Flow Free. We provide mathematical models that can be applied to obtain solutions for these puzzles. In OR/MS lectures, the apps and models can be used as examples or exercises when teaching mathematical programming and for discussion of familiar model types such as shortest path and network flow models. Given the popularity of logic puzzle apps on smartphones, such exercises might be motivating for students. The level of difficulty of the models presented here varies from easy to more difficult.

Puzzle—More Logic Puzzle Apps Solved by Mathematical Programming

“…This article has presented six logic puzzles that are available as smartphone apps, along with mathematical models to solve them. As in Hartmann (2018), the puzzle apps and models are used in the OR lecture in two bachelor of science programs-namely business administration and business informatics. The lecture is given in the fourth semester, after the students have completed basic lectures on mathematics.…”

“…Mathematical programming formulations for Sudoku and related implementations have been published in several scientific journals and books, such as Chlond (2005), Koch (2006), Weiss and Rasmussen (2007), Rasmussen and Weiss (2007), Bartlett et al (2008), and Oki (2012, section 9.1); they also can be found in various blogs. Further puzzles for which mathematical models have been proposed include, among others, the n queens problem (Letavec and Ruggiero 2002), other chessboard placement puzzles Toase 2002, Chlond 2010), Einstein's riddle (Yeomans 2003), logic grid puzzles (Chlond 2014), and the popular smartphone puzzle apps Flow Free (also called Numberlink) and Infinity Loop (Hartmann 2018).…”

“…It might be interesting for students to develop integer programs to solve puzzles. In recent years, a large number of logic puzzles appeared as smartphone apps, and considering the numbers of downloads reported in the app stores, many of the logic puzzle apps are immensely popular (Hartmann 2018). It may be particularly motivating for students to develop mathematical models for logic puzzle apps they can easily download and play on their devices.…”

“…This paper presents six logic puzzles that are available as smartphone apps and develops mathematical programming formulations to solve them. As in Hartmann (2018), the following criteria are used for selecting the puzzles. The first goal is to obtain models with different levels of difficulty, with a particular focus on models that are not too difficult (to use them in introductory lectures).…”

Development and Evaluation of Maze-Like Puzzle Games to Assess Cognitive and Motor Function in Aging and Neurodegenerative Diseases

“…Some cells contain colored circles with numbers or letters (''dots'') that represent start and end points of paths, while the rest of the cells are empty (Kalvelagen, 2017). Dots always come in pairs that have the same color and letter (Hartmann, 2018; see Figure 1, top row). The overall goal of NL puzzles is to connect all pairs of dots with non-intersecting and continuous lines (called ''path'' or ''flow'') such that finally each empty cell in the grid is part of a path (Adcock et al, 2015).…”