190Assignment1

Due Friday 28th July

Question 1

1. (Mindscape 2, Chapter 1 of text) There were 100 politicians at a certain convention.Each politician was either crooked or honest. We are given the following two facts:

• At least one of the politicians was honest.
• Given any two of the politicians, at least one of the two was crooked.

Can it be determined from these facts how many of the politicians were honest and how many were crooked? If so, how many? If not, why not?

Answer

From these facts, we can determine that of the hundred politicians, only one of them is honest. For the second statement, where at least one in a sample of two politicians is crooked, to hold true, there can be no more than one honest politician in population. If there were more than one honest politician in the population the samples are being drawn from, it is possible that a sample of two may not have a crooked politician and thus the second statement would be false.

Question 2

2. (Mindscape 12, Chapter 1 of text) For his 13th birthday, Adam was allowed to travel down to Sarah’s Sporting Goods store to purchase a brand new fishing pole. With great excitement and anticipation, Adam boarded the bus on his own and arrived at Sarah’s store. Although the collection of fishing poles was tremendous, there was only one pole for Adam and he bought it: a 1.5m, one-piece fibreglass “Trout-Troller” fishing pole.

When Adam’s return bus arrived, the driver reported that Adam could not board the bus with the fishing pole. Objects longer than 1.2m were not allowed on the bus. Adam remained at the bus stop holding his beautiful 1.5m pole. Sarah, who has observed the whole ordeal, rushed out and said, “We’ll get your fishing pole on the bus!” Sure enough, when the same bus and the same driver returned, Adam boarded the bus with his fishing pole, and the driver welcomed him aboard with a smile. How was Sarah able to have Adam board the bus with his 1.5m pole without breaking or bending the bus-line rules or the pole?

Answer

It is likely that Adam and Sarah put the fishing rod inside a box to give the illusion of a shorter object. The fishing rod could fit in a 1.2m 'long' box at an angle. The rod itself will still be 1.5m long, as would the box in dimension of the angle the rod is placed in. It could be argued however that in a sense this is still "bending the bus-line rules" and therefore not an acceptable answer.

An alternative solution could be that the one-piece fibreglass rod is telescopic. This is a common feature on rods to cope with transportation. In this solution the object would actually decrease in size without bending the rules or the pole which would still technically be one-piece (It can not be separated into different pieces).

Question 3

3. (Mindscape 13, Chapter 1 of text) Carmilla Snobnosey lifted the delicate Spode teapot and poured exactly 100ml of the aromatic brew into the flowered, shell china teacup. She placed the cream pitcher, also containing exactly 100ml, on the Revere silver tray and carried the offering to Podmarsh Hogslopper. “Would you like some tea and cream, Mr Hogslopper?” she asked. “Yup. Thanks. Ow doggie, sure looks hot. I’d better cool it down with this here milk,” he responded politely, and carefully poured exactly 30ml of cream into his steaming tea and stirred. “That ought to do it,” he said when the steam stopped rising from the tea. “Here, I’ll give you back that there cream.” Whereupon he carefully spooned exactly 30ml from his teacup back into the cream pitcher. Podmarsh blushed as he looked at a tea leaf or two floating in the cream and realized his faux pas. Caught at an awkward pass, he decided to smooth things over with an intriguing puzzle. “Ya know, Mrs Snobnosey, I wonder if the tea is more diluted than the cream, or if the cream is more diluted that the tea?” Write a paragraph or two that gives an answer to Podmarsh’s question. Explain your reasoning carefully.

Answer

There is just as much tea in the cream, as there is cream in the tea. Initialy there is 100ml of tea in the cup and 100ml of milk in the pitcher.

1. 30ml of cream from the pitcher is poured into the cup. This leaves the pitcher with 70ml of pure cream, and the cup with 130ml of liquid consisting of 3 parts milk to 10 parts tea.
2. 30ml of this mixed liquid is then spooned back into the pitcher. This leaves the cup with 100ml of 10 parts tea, to 3 parts cream. The pitcher as 100ml of liquid in total. This is made up of 70ml of pure cream, and 30ml of liquid which is 10 parts tea to 3 parts cream.
3. This means that in the cup, there is 76.9ml of tea, and 23.1ml of cream. In the pitcher there is 76.9ml of cream and 23.1ml of tea.

You would expect the liquid to in the teacup to be tea. As such, any amount of foreign liquid contributes to dilution of the tea. This is mirrored with the pitcher. While the tea cup has the same amount of cream mixed in as the pitcher has tea inside, It could be argued that the pitcher is less diluted because the tea has not been mixed in. In a sense the cream is more pure and therefore less diluted.

Question 4

(Similar to Meanie Genie story, Chapter 1 of text) Alley is given eight identical looking stones and a set of balance scales. One of the stones is lighter than the rest. Explain how Alley can find the lighter stone by using the scales exactly twice.

Answer

The stones can be separated into two groups of three and one group of two.

1. Alleys first step is to weigh the two groups of three stones against each other.
   1. If they are identical, the lighter stone will be one of the remaining two stones. Alley would simply have to weigh these two against each other to find which is the light one
   2. If one group is lighter, the light stone must be in that group of three. This means that the other five stones are all the same weight.

Alley now has to find the stone from a selection of three and can use the scales exactly once more.

1. Alleys second step is to take two of the three stones and weigh them against each other.
   1. If they are identical, the lighter stone will be the last one remaining which wasn't weighed a second time. Otherwise the light stone is the lightest of the two on the scales.

Tutorial Question

Question from tutorial to be handed in with the assignment.

• Tutorial 1 question and answer.