Mastermind is NP-Complete

In this paper we show that the Mastermind Satisfiability Problem (MSP) is NP-complete. The Mastermind is a popular game which can be turned into a logical puzzle called Mastermind Satisfiability Problem in a similar spirit to the Minesweeper puzzle. By proving that MSP is NP-complete, we reveal its intrinsic computational property that makes it challenging and interesting. This serves as an addition to our knowledge about a host of other puzzles, such as Minesweeper, Mah-Jongg, and the 15-puzzle

Separation-Sensitive Collision Detection for Convex Objects

We develop a class of new kinetic data structures for collision detection between moving convex polytopes; the performance of these structures is sensitive to the separation of the polytopes during their motion. For two convex polygons in the plane, let $D$ be the maximum diameter of the polygons, and let $s$ be the minimum distance between them during their motion. Our separation certificate changes $O(\log(D/s))$ times when the relative motion of the two polygons is a translation along a straight line or convex curve, $O(\sqrt{D/s})$ for translation along an algebraic trajectory, and $O(D/s)$ for algebraic rigid motion (translation and rotation). Each certificate update is performed in $O(\log(D/s))$ time. Variants of these data structures are also shown that exhibit \emph{hysteresis}---after a separation certificate fails, the new certificate cannot fail again until the objects have moved by some constant fraction of their current separation. We can then bound the number of events by the combinatorial size of a certain cover of the motion path by balls.Comment: 10 pages, 8 figures; to appear in Proc. 10th Annual ACM-SIAM Symposium on Discrete Algorithms, 1999; see also http://www.uiuc.edu/ph/www/jeffe/pubs/kollide.html ; v2 replaces submission with camera-ready versio

Synthesis of 1-substituted 3-amino-1H-1,2,4-triazoles from ethyl N-(5-phenyl-1,2,4-oxadiazol-3-yl)formimidate

A general and efficient method for the synthesis of 1-substituted 3-amino-1H-1,2,4-triazoles has been developed. The desired 3-amino-1H-1,2,4-triazoles (3) were prepared in good to excellent yields from ethyl N-(5-phenyl-1,2,4-oxadiazol-3-yl)formimidate (1a) and anilines or amines (2) via a one-pot process involving formimidamide formation followed by a thermal monocyclic rearrangement. The benzoyl protecting group could be readily removed by sulfuric acid promoted deprotection