Explanation Given information: starting position consists of three pilescontaining two, two, and one stone, respectively. Calculation: Consider a pile of 1 stone, a pile of 2 stones and a pile of 2 stones (which will be represented in the root by 1 2 2). A player can then pick 1 or more stones from either pile, or merge stones from two piles. A square represent the moves by the first player, while a circle represent the moves by the second player...

Discrete Mathematics And Its Applications 7th Edition

7th Edition

ISBN: 9781259152153

Author: Kenneth H. Rosen

Publisher: MCG CUSTOM

See similar textbooks

Videos

Question

Chapter 11.2, Problem 36E

To determine

Draw the game tree for this variationof nim if the starting position consists of three pilescontaining two, two, and one stone, respectively. Find thevalues of each vertex in the game tree and determine thewinner if both players follow an optimal strategy.

Expert Solution & Answer

Want to see the full answer?

Check out a sample textbook solution

See solution

Chapter 11.2, Problem 35E

Chapter 11.2, Problem 37E

Students have asked these similar questions

T3.2: Prove that if the Graceful Tree Conjecture (every tree has a graceful labeling) is true and T' is a tree with m edges, then K2, decomposes into 2m - 1 copies of T. Hint - Delete a leaf to get 7" and apply the decomposition of K2(m-1)+1 = K2m-1 into T'. Then explain how the decomposition allows the pendant edge to be added to a new vertex to obtain a decomposition of K2m into copies of T.

Use the matrix tree theorem to determine the number of spanning trees of the graphs Kr∨sK1.These are the graphs formed by by adding all edges between a complete graph on r vertices and atrivial graph (no edges) on s vertices.

The maximum capacity spanning tree problem is as follows for a given graph G = (V, E) withcapacities c(uv) on the edges. The capacity of a tree T is defined as the minimum capacity of anedge in T. The maximum capacity spanning tree problem is to determine the maximum capacity ofa spanning tree.(i) Describe how to modify the input graph to find a maximum weight spanning tree making use ofa minimum weight spanning tree algorithm.(ii) Show that a maximum (weight) spanning tree is also a maximum capacity spanning tree.(iii) Is the converse of part (ii) true? That is, is it true that a maximum capacity spanning tree is alsoa maximum spanning tree? Either give counterexamples (of all sizes) or a proof.(iv) Prove the following max-min result. The maximum capacity of a spanning tree is equal to theminimum bottleneck value of a cut. For a subset U ⊆ V , the cut [U, V − U] is the set of edgesbetween U and V − U. The bottleneck value of a cut [U, V − U] is the largest capacity among theedges of…

Chapter 11 Solutions

Discrete Mathematics And Its Applications 7th Edition

Ch. 11.1 - Prob. 1E Ch. 11.1 - Vhich of these graphs are trees?Ch. 11.1 - Prob. 3E Ch. 11.1 - Prob. 4E Ch. 11.1 - Prob. 5E Ch. 11.1 - Prob. 6E Ch. 11.1 - Prob. 7E Ch. 11.1 - Prob. 8E Ch. 11.1 - Prob. 9E Ch. 11.1 - Prob. 10E

Knowledge Booster

Learn more about

Need a deep-dive on the concept behind this application? Look no further. Learn more about this topic, subject and related others by exploring similar questions and additional content below.

Draw the game tree for this variationof nim if the starting position consists of three pilescontaining two, two, and one stone, respectively. Find thevalues of each vertex in the game tree and determine thewinner if both players follow an optimal strategy.

Solution Summary: The author explains how to draw the game tree for this variation of nim if the starting position consists of three piles containing two, two and one stone, respectively.

Videos

Draw the game tree for this variationof nim if the starting position consists of three pilescontaining two, two, and one stone, respectively. Find thevalues of each vertex in the game tree and determine thewinner if both players follow an optimal strategy.

Want to see the full answer?

Chapter 11 Solutions