CS2104: Introduction to Problem Solving
Homework Assignment 11
Due at 8:00AM on Friday, November 04
30 Points
See the General Guidelines for homework assignments. Don't forget to include the pledge statement!
This assignment may optionally be done with a partner. You are strongly advised to use a partner. If you do use a partner, then:
- Partners must work together on the problems, not independently.
- The final submission must contain the name of both partners.
- Only one partner will make the actual submission to Canvas.
- Your submission must explain, for each problem, the contributions of each partner.
- Bottle A contains a quart of milk, and Bottle B contains a quart of coffee. (Note that the bottles themselves are as big as needed.) Pour some amount of B into A, mix well, then pour this amount back into B until both bottles contain a quart of liquid. What is the relationship between fraction of coffee in A and the fraction of milk in B? You must explain your answer.
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Problem (that we did in class):
Assume that every point in the plane is colored either red or blue.
Prove that there exist two points that have the same color and that are
exactly 1 mile apart.
Attempted argument:
- Take an equilateral triangle with sides 1 mile in length.
- By the pigeonhole principle, there must be two points having the same color that are exactly 1 mile apart.
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What is the next letter in the sequence O, T, T, F, F, S, S, E, ...?
What is the rule for obtaining the next letter? -
Find the next member in this sequence:
1, 11, 21, 1211, 111221, 312211, 13112221, 1113213211, ...
What is the rule for obtaining the next member? - Pat wants to take a 1.5-meter-long sword onto a train, but the conductor won't allow it as carry-on luggage. And the baggage person won't take any item whose greatest dimension exceeds 1 meter. What should Pat do?