## Electronic Journal of Probability

- Electron. J. Probab.
- Volume 22 (2017), paper no. 9, 29 pp.

### Mixing time of the fifteen puzzle

Ben Morris and Anastasia Raymer

#### Abstract

We show that the mixing time for the fifteen puzzle in an $n \times n$ torus is on the order of $n^4 \log n$.

#### Article information

**Source**

Electron. J. Probab., Volume 22 (2017), paper no. 9, 29 pp.

**Dates**

Received: 1 September 2016

Accepted: 17 October 2016

First available in Project Euclid: 31 January 2017

**Permanent link to this document**

https://projecteuclid.org/euclid.ejp/1485831705

**Digital Object Identifier**

doi:10.1214/16-EJP11

**Mathematical Reviews number (MathSciNet)**

MR3613702

**Zentralblatt MATH identifier**

1360.60136

**Subjects**

Primary: 60J10: Markov chains (discrete-time Markov processes on discrete state spaces)

**Keywords**

fifteen puzzle mixing time interchange process

**Rights**

Creative Commons Attribution 4.0 International License.

#### Citation

Morris, Ben; Raymer, Anastasia. Mixing time of the fifteen puzzle. Electron. J. Probab. 22 (2017), paper no. 9, 29 pp. doi:10.1214/16-EJP11. https://projecteuclid.org/euclid.ejp/1485831705