DPIT113 Problem Solving 2020 Autumn Assignment 1 Due date: 11:55pm Sunday 5th April 2020

Part A (6 marks):

In this part, you are given a scenario of a problem. You are required to use the knowledge you have learned in the subject so far to solve this problem.

The problem:

After Neo and Morpheus saved the Matrix, they decided to do some investments. After researching, they found that investment on properties is very popular nowadays.

After looking through the market, there is one property which has risen their interests. However, only one of them can be the new owner of this property.

The original owner’s expectation of this property is $100.

The real-estate agent will hold the bidding of this property on Sunday while Neo and Morpheus are the only two potential buyers who will attend this bid. They will take turns placing down a $10, $20, or $50 notes.

Whoever places the note that makes the total $100 is the winner and gets the chance to purchase this property.

1. Draw the state graph showing the allowable states and moves.

2. Label the states as winning or losing positions. Explain your notation.

3. If New goes first, who will win? Please explain your answer.

4. How many different combinations of legal bids adding to $100 are there and how does it relates to the state graph you draw in Q1?

5. Neo doesn’t know this, but Morpheus has $10 and $20 notes, will this change your answer? Please explain your answer.

Part B (4 marks):

You have a row of coins, with 4 head and 3 tails, they are arranged from left to right as follows, where H means the coin is showing heads and T means the coin is showing tails:

H T T H T H H

Each move, you can turn over any two adjacent coins.

1. Explain why it is impossible to solve this problem if the goal state is all coins showing heads.

2. Shown that it is possible to solve this problem if the goal state is all coins showing tails.

Submission:

1. Convert your assignment to pdf format.

2. Upload to Moodle in the Assignment 1 submission box before the due date.

Important: this is an individual assignment

You should complete this assignment without copying from others. Plagiarism, copying someone else’s work, will result in you being given a mark of zero. It doesn’t matter if you copy from as friend or the internet; both count as plagiarism.

Allowing others to plagiarize, by providing them with your own work, it also unacceptable. If assignments are deemed too similar, those assignments will be given a mark of zero. If you need help with an assignment, see your tutor or lecturer in their consultation times.

You can view the UOW College student conduct policy at:

https://www.uowcollege.edu.au/content/groups/public/@web/@uowc/docu ments/doc/uow218734.pdf

Part A (6 marks):

In this part, you are given a scenario of a problem. You are required to use the knowledge you have learned in the subject so far to solve this problem.

The problem:

After Neo and Morpheus saved the Matrix, they decided to do some investments. After researching, they found that investment on properties is very popular nowadays.

After looking through the market, there is one property which has risen their interests. However, only one of them can be the new owner of this property.

The original owner’s expectation of this property is $100.

The real-estate agent will hold the bidding of this property on Sunday while Neo and Morpheus are the only two potential buyers who will attend this bid. They will take turns placing down a $10, $20, or $50 notes.

Whoever places the note that makes the total $100 is the winner and gets the chance to purchase this property.

1. Draw the state graph showing the allowable states and moves.

2. Label the states as winning or losing positions. Explain your notation.

3. If New goes first, who will win? Please explain your answer.

4. How many different combinations of legal bids adding to $100 are there and how does it relates to the state graph you draw in Q1?

5. Neo doesn’t know this, but Morpheus has $10 and $20 notes, will this change your answer? Please explain your answer.

Part B (4 marks):

You have a row of coins, with 4 head and 3 tails, they are arranged from left to right as follows, where H means the coin is showing heads and T means the coin is showing tails:

H T T H T H H

Each move, you can turn over any two adjacent coins.

1. Explain why it is impossible to solve this problem if the goal state is all coins showing heads.

2. Shown that it is possible to solve this problem if the goal state is all coins showing tails.

Submission:

1. Convert your assignment to pdf format.

2. Upload to Moodle in the Assignment 1 submission box before the due date.

Important: this is an individual assignment

You should complete this assignment without copying from others. Plagiarism, copying someone else’s work, will result in you being given a mark of zero. It doesn’t matter if you copy from as friend or the internet; both count as plagiarism.

Allowing others to plagiarize, by providing them with your own work, it also unacceptable. If assignments are deemed too similar, those assignments will be given a mark of zero. If you need help with an assignment, see your tutor or lecturer in their consultation times.

You can view the UOW College student conduct policy at:

https://www.uowcollege.edu.au/content/groups/public/@web/@uowc/docu ments/doc/uow218734.pdf

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