Grade 6 Math Circles
Computer Science - Problem Set

1. Determine the values of each of the variables and their data types after the following code is run.

   a = 17
   b = 5.0
   c = b - a
   d = b * c
   e = (a != d)
   f = not(not(e))
   g = e and not(f)
   b = d

   Solution: We will keep track of each value after each step using the table below:

   	Initial	Line 1	Line 2	Line 3	Line 4	Line 5	Line 6	Line 7	Line 8
   $a$	None	$17$	$17$	$17$	$17$	$17$	$17$	$17$	$17$
   $b$	None	None	$5.0$	$5.0$	$5.0$	$5.0$	$5.0$	$5.0$	$-60.0$
   $c$	None	None	None	$-12.0$	$-12.0$	$-12.0$	$-12.0$	$-12.0$	$-12.0$
   $d$	None	None	None	None	$-60.0$	$-60.0$	$-60.0$	$-60.0$	$-60.0$
   $e$	None	None	None	None	None	$True$	$True$	$True$	$True$
   $f$	None	None	None	None	None	None	$True$	$True$	$True$
   $g$	None	None	None	None	None	None	None	$False$	$False$

   Thus, after the code is run, we have that $a=17$ (int), $b=-60.0$ (float), $c=-12.0$ (float), $d=-60.0$ (float), $e=True$ (bool), $f=True$ (bool) and $g=False$ (bool).

2. Let $a=25$, $b=4$ and $c=9$. Determine the following.

   1. a + b - c

   2. a * (c / b)

   3. (b ** b) + (9 // 4)

   4. (a % b) - (a * b * c)

   Solution:

   1. a+b-c $⟹$ 25+4-9 $⟹$ 29-9 $⟹$ 20

   2. a*(c/b) $⟹$ 25*(9/4) $⟹$ 25*(2.25) $⟹$ 56.25

   3. (b**b)+(c//a) $⟹$ (4**4)+(9//4) $⟹$ 256+2 $⟹$ 258

   4. (a%b)+(a*b*c) $⟹$ (25%4)+(25*4*9) $⟹$ 1-(100*9) $⟹$ 1-900 $⟹$ -899

3. Let $a=3$, $b=-8$, $c=3.0$ and $d=0$. Determine the following.

   1. not(a == c)

   2. (b <= c) and (d > b)

   3. not((a != b) or (d == 0))

   Solution:

   1. not(a==c) $⟹$ not(3==3.0) $⟹$ not(True) $⟹$ False

   2. (b<=c) and (d>b) $⟹$ (-8<=3.0) and (0>-8) $⟹$ True and True $⟹$ True

   3. not((a!=b) or (d==0)) $⟹$ not((3!=-8) or (0==0)) $⟹$ not(True or True) $⟹$ not(True) $⟹$ False

4. The volume of a rectangular prism is determined by multiplying the length, width and height of the rectangular prism by each other. Write a program called rec_prism_volume that inputs the length, width and height of a rectangular prism, and outputs the volume of the rectangular prism.

   Solution:

   def rec_prism_volume(length, width, height):
   
   	volume = length * width * height
   	
   	return volume

5. There are approximately $1.609344$ kilometres in a mile. Write two programs:

   • km_to_miles, inputs a distance in kilometres and outputs the equivalent distance in miles

   • miles_to_km, inputs a distance in miles and outputs the equivalent distance in kilometres

   Use these two programs to make the following conversions. Round to $4$ decimal places.

   1. $1$ km to miles

   2. $10$ miles to km

   3. $120$ km to miles

   4. $54.0592937$ miles to km

   Solution:

   def km_to_miles(km_distance):
   
   	mile_distance = km_distance / 1.609344
   	
   	return mile_distance

   def miles_to_km(mile_distance):
   
   	km_distance = mile_distance * 1.609344
   	
   	return km_distance

   1. $1$ km $=0.6214$ miles

   2. $10$ miles $=16.0934$ km

   3. $120$ km $=74.5645$ miles

   4. $54.0592937$ miles $=87$ km

Bonus Questions

6. Suppose a person writes code that prints the sum of any two inputted numbers. Their code is shown below, but it contains an error. Determine if it is a syntax error or a semantic error, and specify where it occurs. How could this code be fixed? (Hint: Run it through Python Tutor).

   num1 = input('Enter a number:')
   num2 = input('Enter another number:')
   
   sum = num1 + num2
   
   print('The sum of', num1, 'and', num2, 'is', sum)

   Solution: This code contains a semantic error because it uses incorrect logic. The error occurs at the line

   sum = num1 + num2

   Since the values of num1 and num2 are user inputs, the data types of these values is str. So, when the third line of code runs, we have two strings being added together, which results in the value of sum being the value of num1 followed by the value of num2. (e.g. If num1 = "7" and num2 = "6", then sum = "76".

   We can fix this error by adding two lines of code, before sum is defined, where the values of num1 and num2 are converted to int. The correct code is shown below.

   num1 = input('Enter a number:')
   num2 = input('Enter another number:')
   
   num1 = int(num1)
   num2 = int(num2)
   
   sum = num1 + num2
   
   print('The sum of', num1, 'and', num2, 'is', sum)

7. The following code contains a total of $3$ syntax errors. Identify each of them.

   a == input("Enter a number:")
   b = int(a)
   c = a + b
   a = int(a)
   d = 0
   e = a / d

   Solution: Here are the syntax errors in the code:

   1. The first line uses == and not =, which means that instead of defining the value of $a$ to be the user inputted value, we are comparing the value of $a$ to the user inputted value. Since $a$ hasn’t been defined yet, we get a syntax error.

   2. The third line adds the value of $a$, which is str, and the value of $b$, which is int, which causes a syntax error.

   3. The sixth line divides the value of $a$ by the value of $d$, which is $0$, thus a division by $0$ causes a syntax error.