Abstract Puzzle Generators and Symmetric Puzzle Layout.pdf
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Puzzle Generators and Symmetric Puzzle Layout
Kozo Sugiyama1, Ryo Osawa1 and Seok-Hee Hong2
1 School of Knowledge Science, Japan Advanced Institute of Science and Technology, Asahidai 1-1,
Tatsunokuchi, Nomi, Ishikawa, 923-1292, Japan
{Sugi, R-osawa}@jaist.ac.jp
2 National ICT Australia; School of Information Technologies, The University of Sydney,
Sydney, NSW 2006, Australia
shhong@.au
Abstract
We present two abstract models of puzzles, permutation
puzzles and cyclic puzzles, which can be modelled as
puzzle graphs. Based on these models, we implement two
puzzle generators and produce various layouts of the
puzzles using graph drawing algorithms. Using these
puzzle generators we can create new puzzles. Further, we
can create new user interfaces of a puzzle by applying
different layout algorithms. We implement a method for
constructing symmetric layouts of puzzles, as symmetry is
the most important aesthetic criteria for the puzzle layout.
Keywords: Puzzle generator, Symmetric layout
1 Introduction
Puzzles have sophisticated logical structures, beautiful
shapes, and attractive user interfaces. To invent new
puzzles and to design new interfaces of puzzles, we have
carried out a systematic approach called ‘divergence via
abstraction’ (Maeda, Sugiyama and Mase 2002a, 2002b;
Sugiyama, Hong and Maeda 2003; Sugiyama, Maeda and
Mizumoto 2003; Sugiyama, Maeda, Osawa and Mizumoto
2005). The basic idea of the approach is illustrated in
Figure 1. Here existing popular puzzles are abstracted and
converted into other media such as graphs, blocks, sounds,
and robots, while preserving their logic. Using this
approach, we can create new puzzles and new interfaces
for puzzles. Our approach closely relates to the creativity
theory called ‘Equivalent Transforming Thinking’
proposed by Ichikawa (Ichikawa 1970).
In this paper, we are mainly concerned with conversions of
puzzles into graphs. More specifically, we consider two
classes of puzzles,
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