The Game of End-Nim
نویسندگان
چکیده
In the game of End-Nim two players take turns in removing one or more boxes from a string of non-empty stacks. At each move boxes may only be taken from the two stacks which form the ends of the string (unless only one stack remains!). We give a solution for both impartial and partizan versions of the game and explain the significance of the mystic hieroglyphs:
منابع مشابه
Some Remarks on End-Nim
We reexamine Albert and Nowakowski’s variation on the game of Nim, called End-Nim, in which the players may only remove coins from the leftmost or rightmost piles. We reformulate Albert and Nowakowski’s solution to this game. We examine its misère version and a further variant where the winner is the player who reduces the game to a single pile; we call this Loop-End-Nim. We show that the three...
متن کامل# G 2 Integers 15 ( 2015 ) an Atlas of N - and P - Positions in ‘ Nim with a Pass ’
Perhaps the most famous combinatorial game is Nim, which was completely analyzed by C.L. Bouton in 1902. Since then, the game of Nim has been the subject of many research papers. In Guy and Nowakowski’s Unsolved Problems in Combinatorial Games, the following entry is found: “David Gale would like to see an analysis of Nim played with the option of a single pass by either of the players, which m...
متن کاملBuilding Nim
The game of nim, with its simple rules, its elegant solution and its historical importance is the quintessence of a combinatorial game, which is why it led to so many generalizations and modifications. We present a modification with a new spin: building nim. With given finite numbers of tokens and stacks, this two-player game is played in two stages (thus belonging to the same family of games a...
متن کاملA PSPACE-complete Graph Nim
We build off the game, NimG [7] to create a version named Neighboring Nim. By reducing from Geography, we show that this game is PSPACE-hard. The games created by the reduction share strong similarities with Undirected (Vertex) Geography and regular Nim, both of which are solvable in polynomial-time. We show how to construct PSPACE-complete versions with nim heaps ∗1 and ∗2. This application of...
متن کاملPilesize Dynamic One-pile Nim and Beatty’s Theorem
In [4] we proved a generalization of Beatty’s Theorem which we stated came from the Nim value analysis of a game. In this paper we give the Nim value analysis of this game and show its relationship with Beatty’s Theorem. The game is a one-pile counter pickup game for which the maximum number of counters that can be removed on each successive move changes during the play of the game. The move si...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
عنوان ژورنال:
- Electr. J. Comb.
دوره 8 شماره
صفحات -
تاریخ انتشار 2001