190Tutorial1

Questions

1. (Mindscape 1, Chapter 1 of the textbook). Suppose that Don Brash and Helen Clark each have the same amount of money in their pockets. How much must Don give to Helen so that Helen would have $10 more than Don?

Answer

5$

2. (Mindscape 5, Chapter 1 of the textbook). There are two boxes: one marked A and one marked B. Each box contains either $1 million or a deadly snake that will kill you instantly. You must open one box. On box A there is a sign that reads: “At least one of these boxes contains $1 million.” On box B there is a sign that reads: “A deadly snake that will kill you instantly is in box A.” You are told that either both signs are true or both are false. Which box do you open? Be careful, the wrong answer is fatal!

Answer

Box 2

3. (Mindscape 6, Chapter 1 of the textbook). Two rooms are connected by a hallway that has a bend in it so that it is impossible to see one room while standing in the other. One of the rooms has three light switches. You are told that exactly one of the switched turns on a light in the other room, and the other two are not connected to any lights. What is the fewest number of times you would have to walk to the other room to figure out which switch turns on the light? And the follow-up question is: Why is the answer to the preceding question “one”? (Look out, this question uses properties of real lights as well as logic.)

Answer

1, Bulb heats up.

4. Write up your answer to this Mindscape and hand it in with your answers to Assignment 1 (due Friday July 28th). See below for instructions on writing tutorial reports. Don’t forget to write down the names of the people in your tutorial group, so that you can acknowledge your collaborators in your report. (Mindscape 11, Chapter 1 of the textbook). Three strangers, Bob, Mary, and Ivan, meet at a taxi stand and decide to share a cab to cut down on the cost. Each has a different destination, but all the destinations are on the highway leading from the airport, so no circuitous driving is required. Bob’s destination is 10 kilometres away, Mary’s is 20 kilometres, and Ivan’s is 30 kilometres. The taxi costs $1.50 per kilometre, regardless of the number of passengers. How much should each person pay? (Caution: there is more than one way of looking at this situation. A good place to start would be to discuss what would be a fair way to divide the costs.)

Answer

Tutorial Answer to hand in with assignment 1

5. (Mindscape 14, Chapter 1 of the textbook). This one is harder. Only attempt it if you have answered all the other puzzles and still have time for more. Stacy and Sam Smyth were known for throwing a heck of a good party. At one of their wild gatherings, five couples were present (this included the Smyth’s, of course). The attendees were cordial, and some even shook hands with other guests. Although we have no idea who shook hands with whom, we do know that no one shook hands with themselves and no one shook hands with his or her spouse. Given these facts, a guest might not shake anyone’s hand or might shake as many as eight other people’s hands. At midnight, Sam Smyth gathered the crowd and asked the nine other people how many hands each of them had shaken. Much to Sam’s amazement, each person gave a different answer. That is, someone didn’t shake any hands, someone else shook one hand, someone else shook two hands, someone else shook three hands, and so forth, down to the last person, who shook eight hands. Given this outcome, determine the exact number of hands that Stacy Smyth shook.

Answer

She shakes 4 hands, (half). Solve by drawing who shakes hands with who.