[1]
(a) True
(b) True
(c) False
(d) True
(e) True

[2]
(a) 1.0
(b) 0.0
(c) 3
(d) -1.0
(e) 12
(f) 5.0 
(g) 1.0

[3]
12
21
30
---
20
32
---
30
45
---

Note: output from the different values of n in the outer loop (3,4,5) is
separated by ---. The values between the marks correspond to the outputs
of the inner loop, where m takes on values (4,7,10), (5,8), and (6,9).

[4]
10
12
12
14
14
16
16
18
18

Note: n starts at 10, increments by 2, and is printed at both beginning 
(pre increment) and end (post increment) of the while loop. The break 
statement exits the while loop when n reaches 20; the last value printed,
18, is the pre increment value of n.

[5]
First solution (using a break statement):
======================================================================
# Alberto Maria Segre
# Modified HOTPO1 solution

# Read in the number
n = int(raw_input("Enter a number: "))

# We'll use count to tally the HOTPO steps.
count = 0

# The HOTPO process ends normally when n reaches 1.
while (n > 1):
    # Limit number of HOTPO steps allowed.
    if (count > 25):
        break

    # Proceed: handle even/odd increment.    
    if n%2 == 0:
        n = n/2
    else:
        n = (3*n + 1)
    count = count + 1

# At this point, n will be 1 only if you successfully 
# completed the HOTPO process.
if (n == 1):
    print count
else:
    print "HOTPO process aborted!"
======================================================================

Second solution (using a Boolean operation in the while condition):
======================================================================
# Alberto Maria Segre
# Modified HOTPO1 solution

# Read in the number
n = int(raw_input("Enter a number: "))

# We'll use count to tally the HOTPO steps.
count = 0

# The HOTPO process ends normally when n reaches 1; here,
# we'll also limit the number of HOTPO steps allowed.
while (n > 1) and (count <= 25):
    if n%2 == 0:
        n = n/2
    else:
        n = (3*n + 1)
    count = count + 1

# At this point, n will be 1 only if you successfully 
# completed the HOTPO process.
if (n == 1):
    print count
else:
    print "HOTPO process aborted!"