Hostname: page-component-76fb5796d-2lccl Total loading time: 0 Render date: 2024-04-26T10:28:14.277Z Has data issue: false hasContentIssue false
  • English
  • Français

Open questions on Tantrix graphs

Published online by Cambridge University Press:  03 February 2017

Heidi Burgiel  and
Mahmoud El-Hashash
Heidi Burgiel
Affiliation:
Department of Mathematics, Bridgewater State University, Bridgewater, MA, 02325, USA e-mails: hlb@mit.edu
Mahmoud El-Hashash
Affiliation:
Department of Mathematics, Bridgewater State University, Bridgewater, MA, 02325, USA e-mails: hlb@mit.edu
Rights & Permissions [Opens in a new window]

Extract

Core share and HTML view are not available for this content. However, as you have access to this content, a full PDF is available via the ‘Save PDF’ action button.

TantrixTM tiles are black hexagons imprinted with three coloured paths [1] joining pairs of edges. There are three different kinds of path. One is a straight line going from an edge to the opposite edge, one a circular arc joining adjacent edges and one an arc of larger radius joining alternate edges (or two apart). Tiles can be rotated but, since they are opaque, they cannot be turned over. A careful enumeration would indicate that, identifying tiles under rotation but not under reflection, there are 16 such tiles. However, the two tiles consisting of three straight lines (meeting at the centre of the hexagon) are not part of the set, so actually there are only 14 different tiles. The game is played by matching tiles to connect paths of the same colour; the goal is to create loops or long paths of a single colour This easy to learn yet hard to master game has inspired research on strategy (e.g. [2]) and complexity (e.g. [3]).

Type
Articles
Information
The Mathematical Gazette , Volume 101 , Issue 550 , March 2017 , pp. 83 - 89
Copyright
Copyright © Mathematical Association 2017 

References

1. Colour of Strategy, Pohara, Tantrix (2016), available at http://www.tantrix.com Google Scholar
2. Downing, K., Tantrix: a minute to learn, 100 (genetic algorithm) generations to master, Genetic Programming and Evolvable Machines 6 (4) (2005) pp. 381–406.CrossRefGoogle Scholar
3. Holzer, M. and Holzer, W., TantrixTM rotation puzzles are intractable, Discrete Appl. Math. 144 (3) (2004) pp. 345–358.CrossRefGoogle Scholar
4. Burgiel, H. and El-Hashash, M.. The permutahedron πn is Hamiltonian, Int. J. Contemp. Math. Sci. 4 (1) (2009) pp. 31–39.Google Scholar
5. Ziegler, G. M., Lectures on Polytopes, Graduate Texts in Mathematics, Vol. 221, Springer-Verlag, New York (1995), available at http://dx.doi.org/10.1007/978-1-4613-8431-1 CrossRefGoogle Scholar
6. Perfect, H., Concerning arrangements in a circle, Math. Gaz. 40 (February 1956) pp. 45–46.CrossRefGoogle Scholar