ENGR 110: INTRODUCTION TO ENGINEERING Science, Engineering & Mathematics-Cerrito

Question

ENGR 110: INTRODUCTION TO ENGINEERING Science, Engineering & Mathematics-Cerritos College Homework Assignment #10-Due April 14t, 2017 Questions on problem solving 1. Exercise 7.56: Four mathematicians have the following conversation: Alice: I am insane. Bob: I am pure. Charlie: I am applied. Dorothy: I am sane. Alice: Charlie is pure. Bob: Dorothy is insane. Charlie: Bob is applied. Dorothy: Charlie is sane. You are also given that: Pure mathematicians tell the truth about their beliefs. Applied mathematicians lie about their beliefs. Sane mathematicians' beliefs are comect. Insane mathematicians' beliefs are incorrect. Describe the four mathematicians. 2. Exercise 7.58: Tom is from the Census Bureau, and greets Mary at her door. They have the following conversation Tom: I need to know how old your three kids are. Mary: The product of their ages is 36. Tom: l still do not know their ages. Mary: The sum of their ages is the same as my house number. Tom: l still do not know their ages. Mary: The younger two are twins. Tom: Now I know their ages! Thanks! How old are Mary's kids, and what is Mary's house number?

Explanation / Answer

1. Notice that a pure mathematician will always describe his or herself as sane (regardless of his or her actual sanity). Meanwhile an applied mathematician will always describe his or herself as insane. Therefore Alice is applied and Dorothy is pure. In a similar fashion we can reason that Charlie is insane, and Bob is sane. Now Dorothy’s statement that “Charlie is sane” is incorrect, and since we know Dorothy is pure we reason that she is also insane. Then Bob was correct when he stated “Dorothy is insane”, and since we know him to be sane he must also be pure. Thus Charlie was incorrect when he stated ”Bob is applied”, and since we know Charlie to be insane he must also be pure. Finally that means Alice was correct when she stated “Charlie is pure”, and since we already know she is applied, she must also be insane.

2.

From the statement "the product of their ages is 36" the possibilities of the three individual ages are:

1, 1, 36
1, 2, 18
1, 3, 12
1, 4, 9

1, 6, 6
2, 2, 9
2, 3, 6
3, 3, 4

From the statement "the sum of their ages is the same as my house number," it is possible to eliminate all but two possibilities. The sums of these answers we can eliminate are "unique" and if any of them were the house number, then Tom would have then known the ages of the kids!

For example if Mary's house number were 38 he would know that the ages must be 1, 1, and 36!
If her house number were 21, he would know that the ages must be 1, 2, and 18.
If her house number were 10, Tom would know that the ages of her kids must be 3, 3, 4 etc.

So, because of this, these six possibilities can all be eliminated:

1, 1, 36 = 38
1, 2, 18 = 21
1, 3, 12 = 16
1, 4, 9 = 14
2, 3, 6 = 11
3, 3, 4 = 10

The only two remaining possibilities are 1, 6, 6, and 2, 2, 9. (Mary's house number is therefore 13 which is why at this point Tom says, "I still don't know their ages.")

After the clue "the younger two are twins" you can obviously eliminate 1, 6, 6. The only remaining possibility is then 2, 2, 9!

Of course if Mary had said "the older two are twins" then the answer would indeed be 1, 6, 6!!

4. '

First man 1 and man 2 walk across the bridge. This takes 2 minutes.
After this, man 1 walks back with the flashlight. This takes 1 minute.
Then man 3 and man 4 walk across the bridge. This takes 10 minutes.
After this, man 2 walks back with the flashlight. This takes 2 minutes.
Then man 1 and man 2 walk across the bridge. This takes 2 minutes as before.
In total: 2+1+10+2+2=17 minutes.

1, 1, 36
1, 2, 18
1, 3, 12
1, 4, 9

1, 6, 6
2, 2, 9
2, 3, 6
3, 3, 4

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