Dice Rolling: The Movie (2007)

a comedic short film by Erik Demaine and Martin Demaine

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photo of inside the box
This 3.5-minute film accompanies a paper about dice-rolling puzzles (written with Kevin Buchin, Maike Buchin, Dania El-Khechen, Sándor Fekete, Christian Knauer, André Schulz, and Perouz Taslakian), and was originally screened at CCCG 2007 when we presented the paper. Our goal is to introduce more humor into mathematics.

At the comedic/performance level, the film features Erik rolling Martin around in a cardboard box which, as shown on the right, has no special padding inside. Needless to say, this was rather painful, so everything was done in a single take. To guarantee realism, there is no camera motion (or camera operator).

At the mathematical level, the rolling sequence demonstrated in the film (either the “originally intended” 2×3 cycle or the finally executed 2×2 cycle) illustrate a key property of rolling dice: it is possible to change the orientation of the cube without changing the location. In the example, we initially see the 1, 2, and 3 sides of the die, and by the end, we see the 5, 4, and 1 sides. These orientation-changing cycles serve as an important “gadget” in our proof that dice-rolling puzzles are NP-complete. At a more basic level, the film also illustrates our intended notion of rolling a cube—rotating 180° around one of the base edges to fall onto an adjacent square (instead of e.g. rotating in place).

This film was part of the Curved Crease Sculpture exhibition at Guided By Invoices in Chelsea, New York City, January 19–March 3, 2012.

Short Cut

In a rush? Watch this 1.5-minute cut. (No subtitles available.)


This short outtake reel illustrates a few failed attempts in making this film, mainly relating to cardboard-box technology. In the final box, Martin had to tie the top shut, in order to prevent the momentum from opening the top.


written, directed, and acted by Erik Demaine and Martin Demaine
logging and editing by Tom Buehler
Japanese translation by Ryuhei Uehara

Last updated August 13, 2012 by Erik Demaine.