The game of nim is played with a collection of piles of stic

Assignment Help Basic Computer Science

Reference no: EM13696134

The game of Nim is played with a collection of piles of sticks. In one move a player may remove any nonzero number of sticks from a single pile. The players alternately take turns making moves. The player who removes the very last stick loses. Say that we have a game position in Nim with k piles containing s1 , -. ., Sk sticks. Call the position balanced if, when each of the numbers si is written in binary and the binary numbers are written as rows of a matrix aligned at the low order bits, each column of bits contains an even number of is. Prove the following two facts.
a. Starting in an unbalanced position, a single move exists that changes the position into a balanced one.
b. Starting in a balanced position, every single move changes the position into an unbalanced one.

Reference no: EM13696134

Questions Cloud

Write a brief description of physical therapy : Write a general answer to the question. Support your answer with 3 arguments (one intuitive, one inductive, and one deductive). Clearly indicate at the start of each argument what type of argument it is.

Ordering system deployment diagram : At a minimum, your diagram should include nodes for a client, web server, application server, and a data server. In addition, include software components (a COTS package, a DBMS, and a web browser) and place them on the appropriate node. Depict..

Discuss how current or potential employers : From the e-Activity, discuss how current or potential employers might be able to use the information you found and possible steps that could be taken to help ensure your privacy. Provide specific examples to support your response.

Summarize by outlining the sequence of operations : Explain how an operating system can temporarily pass control of the CPU over to user code without risking an indefinite loss of control. Discuss the roles of timer interrupts, privileged mode operation, and memory protection and explain why all of..

The game of nim is played with a collection of piles of stic : The game of Nim is played with a collection of piles of sticks. In one move a player may remove any nonzero number of sticks from a single pile. The players alternately take turns making moves. The player who removes the very last stick loses. Say..

Describe how concepts such as risc : In this six pages research paper, you will investigate the evolution of and current trends in improving system performance with concepts such as RISC, pipelining, cache memory, and virtual memory. In this paper you must, as part of your conclus..

Prevent race conditions in kernel code for a uni-processor : In early Unix kernels the approach used to avoid race conditions in kernel code was to use a combination of the following two techniques: (i) non- preemptive scheduling of threads when they are running in privileged mode and (ii) interrupt disabli..

Perform dynamic address translation : Perform dynamic address translation

Computer forensics examiner get involved with, and how : Other than the two basic types of computer crimes above, what non-computer crimes might a computer forensics examiner get involved with, and how?

User Account

All Pages