15-110 PS8 Sample Solutions - Spring 2018

1. 

(a) - means negation, ^ means and, v means or:
 
   -A ^ B ^ -C ^ -D (for 4)
   v
   -A ^ B ^ -C ^ D (for 5)
   v
   -A ^ B ^ C ^ -D (for 6)
   v
   A ^ -B ^ -C ^ -D (for 8)
   v
   A ^ -B ^ -C ^ D (for 9)

(b) - ( (-A ^ B ^ -C ^ D) v (-A ^ B ^ C ^ -D) )

2.  Computers execute instructions in binary. An interpreter 
    allows us to write in a language we can read and it will 
    translate to binary instructions for us that the computer
    can execute.

3. 

(a) Sequence: (1) 0 5 12 9 8 13 4 1 ,    Period = 8

(b) The last digit repeats after every 10 numbers so the 
    next number will end with a 4.

4.

(a) return randrange(1,11)

(b) return randrange(5, 101, 5)   OR   return randrange(1, 21) * 5

(c) return 2 ** randrange(1, 7)   OR   return 2 ** randrange(0,6) * 2   OR
    return 2 ** (randrange(6) + 1)

(d) cube = ["A" "K", "Q", "J", "10", "9"]
    return cube[randrange(0,6)]

5.

(a) In the total update, the dice are re-rolled so we're not adding 
    the values that were tested in the if statement.

(b) die1 = roll()
    die2 = roll()
    if die1 != die2:
         total = total + die1 + die2
    else
         total = 0

6.

(a) deck[randrange(26,52)]   OR   deck[randint(26,51)]   OR
    sample(deck[26:],1)[0]   OR   choice(deck[26:])

(b) hand[0][0]==hand[1][0]==hand[2][0]==hand[3][0]

    hand[1][0]==hand[2][0]==hand[3][0]==hand[4][0]

    Clever solution:

    hand[0][0]==hand[3][0]

    hand[1][0]==hand[4][0]