A class of games characterized as K-dimensional tic-tac-toe, with paths of length [n], is examined. Best known of these are Tic-Tac-Toe and QUBIC. Some little known results are presented. The results demonstrate a pivotal role for the game of QUBIC, the smallest nontrivial member of the class. An investigation aimed at a solution to the game of QUBIC is then described and some facts and methods are presented. The methods deal primarily with techniques for reducing the opening and end-game to manageable proportions. The mid-game remains as a difficult problem. A program has been written to play QUBIC using the methods discovered. It is able to find extremely long forcing sequences (31 half moves observed). Improvements to the program are planned to allow a human QUBIC player to work with the program in developing mid-game strategies. 25 pp. Ref.
This report is part of the RAND Corporation Paper series. The paper was a product of the RAND Corporation from 1948 to 2003 that captured speeches, memorials, and derivative research, usually prepared on authors' own time and meant to be the scholarly or scientific contribution of individual authors to their professional fields. Papers were less formal than reports and did not require rigorous peer review.
This document and trademark(s) contained herein are protected by law. This representation of RAND intellectual property is provided for noncommercial use only. Unauthorized posting of this publication online is prohibited; linking directly to this product page is encouraged. Permission is required from RAND to reproduce, or reuse in another form, any of its research documents for commercial purposes. For information on reprint and reuse permissions, please visit www.rand.org/pubs/permissions.
The RAND Corporation is a nonprofit institution that helps improve policy and decisionmaking through research and analysis. RAND's publications do not necessarily reflect the opinions of its research clients and sponsors.