Course Content for This Week

    This week's course content has been somewhat fascinating, however, some aspects are still quite tedious to me. My applied study strategies from last week have been quite effective in allowing me to see the fun in each logic problem. Questions involving switching from English to symbolic form and back are certainly some of my favorites. In addition, I have been completing the answers for Assignment 1 with much ease. The tedium occurs in my slight difficulty with the logic laws such as communicative, associative, and distributive laws. This is not due to my inability to see each pattern and why each rule works, it is simply because of the way I look at each statement. I believe that I could figure out each identity on the go without needing to memorize the patterns. I am far more interested in knowing why things work than memorizing patterns and types of questions. However, it may be the unfortunate case that I must memorize these in order to save time and brain power on tests and exams. Only future quizzes and tests will be indicators of this.

Streetcar Drama Solution Attempt

Streetcar Drama (from lecture slides) Solution Attempt

I approached this problem by first assuming that person B has 3 children, all older than 1, with each age a positive integer and one eldest, so I need to find 3 integers. The product of all ages is equal to 36 and I set the sum of all ages equal to the variable y. I then set the age of Child 1 to the variable a, the age of Child 2 to the variable b, and the age of Child 3 to the variable c. Initially, my instincts told me to look for clues while attempting to use 3 variable substitution.

I started thinking about possible situations, perhaps person B has twins or even triplets. Person B must have either one eldest and two younger twins, or children all of different ages. I ruled out triplets because the children's ages could not be equal to a cube root of 36 while remaining an integer. I also disregarded the addition of the eldest child playing piano because I felt that it was unnecessary.

I then thought about possible ways that person A might not be able to figure out the ages based on 2 equations, which are:

In the case of all different ages:

a × b × c = 36
a + b + c = y

In the case of one eldest and two younger twins:

In this case a = c, so we can write a in place of c
a × a × b = 36
a + a + b =y


Because of person A's response to the sum of the ages ("That still doesn't tell me how old they are."), it seems clear that this wasn't enough information for person A to use algebra and solve. In the case of twins and one older child, person B should have been able to use substitution to solve (2 unknowns in each of the 2 equations). But she or he did not, which leads me to believe that there must have been 3 unknowns in each of the 2 equations (one can not use algebra to solve this).

This completely stumped me until I began writing factors of 36.

2 × 18
4 × 9
4 × 3 × 3
2 × 2 × 9
2 × 2 × 3 × 3
3 × 12
3 × 2 × 6

I then realized that 3, 2, and 9 are the only set of 3 factors of 36 with all different values. I concluded that these must be the ages of each child.

This being said, I believe my solution is flawed, because if I assume that Person A could potentially do 2 variable substitution using mental math, it would also be reasonable to assume that he or she could figure out 3 different factors that multiply to 36.

Overcoming Frustration with Logic Questions

    Spending the past two weeks on basic logic in CSC165 has been incredibly tedious and somewhat annoying to me. Although I fully understand the necessity for these core ideas, I still find myself more thrilled by challenging problems such as, "Streetcar Drama" (presented several lectures ago). I'm working to appreciate these concepts, completing all given questions as fast as possible and reading ahead in the course notes, in an attempt to find pleasure in the completion of each new question. I felt that this week's tutorial as well as the quiz were exceptionally easy partially due to my study habits. I'm quite sure that with continued commitment to the course material, the level of difficulty will remain manageable for me.