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Another bridge between Nim and Wythoff
"... The P positions of both twoheap Nim and Wythoff’s game are easy to describe, more so in the former than in the latter. Calculating the actual G values is easy for Nim but seemingly hard for Wythoff’s game. We consider what happens when the rules for removing from both heaps are modfied in various w ..."
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Cited by 7 (3 self)
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The P positions of both twoheap Nim and Wythoff’s game are easy to describe, more so in the former than in the latter. Calculating the actual G values is easy for Nim but seemingly hard for Wythoff’s game. We consider what happens when the rules for removing from both heaps are modfied in various
A generalized diagonal Wythoff Nim
, 2011
"... The Ppositions of the wellknown 2pile takeaway game of Wythoff Nim lie on two ‘beams ’ of slope √ 5+1 ..."
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Cited by 6 (5 self)
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The Ppositions of the wellknown 2pile takeaway game of Wythoff Nim lie on two ‘beams ’ of slope √ 5+1
Wythoff Nim Extensions and Splitting Sequences
"... We study extensions of the classical impartial combinatorial game of Wythoff Nim. The games are played on two heaps of tokens, and have symmetric move options, so that, for any integers 0 ≤ x ≤ y, the outcome of the upper position (x, y) is identical to that of (y, x). First we prove that φ−1 = 2 ..."
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We study extensions of the classical impartial combinatorial game of Wythoff Nim. The games are played on two heaps of tokens, and have symmetric move options, so that, for any integers 0 ≤ x ≤ y, the outcome of the upper position (x, y) is identical to that of (y, x). First we prove that φ−1 = 2
MAHARAJA NIM  WYTHOFF’S QUEEN MEETS THE KNIGHT
, 2010
"... New combinatorial games are introduced, of which the most pertinent is Maharaja Nim. The rules extend those of the wellknown impartial game of Wythoff Nim in which two players take turn in moving a single Queen of Chess on a large board, attempting to be the first to put her in the lower left corne ..."
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Cited by 2 (2 self)
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New combinatorial games are introduced, of which the most pertinent is Maharaja Nim. The rules extend those of the wellknown impartial game of Wythoff Nim in which two players take turn in moving a single Queen of Chess on a large board, attempting to be the first to put her in the lower left
The game of EndWythoff
"... ABSTRACT. Given a vector of finitely many piles of finitely many tokens. In EndWythoff, two players alternate in taking a positive number of tokens from either endpile, or taking the same positive number of tokens from both ends. The player first unable to move loses and the opponent wins. We char ..."
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Cited by 4 (1 self)
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ABSTRACT. Given a vector of finitely many piles of finitely many tokens. In EndWythoff, two players alternate in taking a positive number of tokens from either endpile, or taking the same positive number of tokens from both ends. The player first unable to move loses and the opponent wins. We
Extensions of Wythoff’s Game
, 2013
"... We determine the maximal set of moves for 2pile takeaway games with prescribed Ppositions (⌊αn⌋, ⌊βn⌋) for n ∈ Z≥1 where α ∈ (1, 2) is irrational, 1/α+1/β = 1. This was done in [3] for the special case α = golden ratio. We generalize the infinite Fibonacci word to an infinite word W with alphabet ..."
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We determine the maximal set of moves for 2pile takeaway games with prescribed Ppositions (⌊αn⌋, ⌊βn⌋) for n ∈ Z≥1 where α ∈ (1, 2) is irrational, 1/α+1/β = 1. This was done in [3] for the special case α = golden ratio. We generalize the infinite Fibonacci word to an infinite word W with alphabet Σ = {a, b}, in which α replaces the golden ratio, and we analyze the set {s ∈ Z≥0: W(s) = b, W(s + x) = a} for any fixed value of x. 1
Adjoining to Wythoff 's Game its Ppositions as Moves
 Theoret. Comp. Sci. 205
, 1998
"... . A rewarding method for generating a new game \Gamma i+1 from a known game \Gamma i is to adjoin an appropriate subset of the P positions (2nd player winning positions) of \Gamma i to \Gamma i+1 as moves. We illustrate this statement by adjoining to the generalized Wythoff Game three subsets of it ..."
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Cited by 5 (0 self)
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. A rewarding method for generating a new game \Gamma i+1 from a known game \Gamma i is to adjoin an appropriate subset of the P positions (2nd player winning positions) of \Gamma i to \Gamma i+1 as moves. We illustrate this statement by adjoining to the generalized Wythoff Game three subsets
A CLASS OF WYTHOFFLIKE GAMES
"... We present a class of twoplayer Wythoff game variations we dub Wyt(f) that depends on a given function f(k). In this class a move consists of removing either a positive number of tokens from precisely one of two given piles, or k tokens from one pile and ℓ from the other, subject to the constraint ..."
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We present a class of twoplayer Wythoff game variations we dub Wyt(f) that depends on a given function f(k). In this class a move consists of removing either a positive number of tokens from precisely one of two given piles, or k tokens from one pile and ℓ from the other, subject to the constraint
The First Forty Wythoff Pairs n  1
"... In this paper we point out another of those fascinating "coincidences " which are so characteristically associated with the Fibonacci numbers. It occurs in relation to the socalled safe pairs (an, bn) for Wythoffs Nim [1, 2, 3]. These pairs have been extensively analyzed by Carlitz, Scovi ..."
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In this paper we point out another of those fascinating "coincidences " which are so characteristically associated with the Fibonacci numbers. It occurs in relation to the socalled safe pairs (an, bn) for Wythoffs Nim [1, 2, 3]. These pairs have been extensively analyzed by Carlitz
Results 1  10
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