18. Loops — Homework solutions

The .py solution files are in exercises/18/homework/solutions/.

Problem 1 — Count to 20

Problem. Print 1 through 20 with a while loop.

How to think about it. A while loop needs a start value, a stop condition, and an update. Start at 1, stop past 20, add 1 each pass.

Worked solution.

i = 1
while i <= 20:
    print(i)
    i = i + 1

Common mistakes.

  • Forgetting i = i + 1. The condition stays True forever, so the loop never ends.
  • Using i < 20, then missing 20. <= includes the endpoint.

Problem 2 — Multiplication table of 7

Problem. Print 7 * i = result for i from 1 to 12.

How to think about it. A for loop with range(1, 13). Each pass prints a line from i and 7 * i.

Worked solution.

for i in range(1, 13):
    print(f"7 * {i} = {7 * i}")

Common mistakes.

  • Writing range(1, 12). That stops at 11 and misses the last line. range(start, stop) excludes stop, so use range(1, 13) to reach 12.
  • Confusing 7 * i (printed) with i (the counter).

Problem 3 — Stop at the threshold

Problem. Add 1, 2, 3, ... to a total. Stop once it exceeds 100. Print the counter and the total.

How to think about it. Two variables: a counter that grows by 1 each pass, and a total that grows by the counter. The exit, total > 100, fits inside as if ... break, which suits while True:.

Worked solution.

i = 1
total = 0

while True:
    total = total + i
    if total > 100:
        break
    i = i + 1

print("Stopped at i =", i, "with total =", total)

For i = 1..14, the sum 1+2+...+14 = 105 is the first total over 100:

Stopped at i = 14 with total = 105

Common mistakes.

  • Adding i = i + 1 before adding to total. That adds the next i, not the current. Order them on purpose.
  • Putting the break after i = i + 1. Then the printed i is one past the value that pushed the total over 100. Either works; be deliberate.

Challenge — Sum 1..N

Problem. Read n, sum 1..n with a for loop, compare with the closed form n * (n + 1) // 2.

How to think about it. A for loop from range(1, n + 1) adds each counter to a total. The closed form for the first n positive integers is n * (n + 1) // 2, Gauss's trick. Print both, confirm they match.

Worked solution.

n = int(input("Enter a positive whole number n: "))

total = 0
for i in range(1, n + 1):
    total = total + i

print(f"Sum from 1 to {n} is {total}")
print("Formula gives", n * (n + 1) // 2)

// is integer division, so both lines show whole numbers. Expected.

Common mistakes.

  • Writing range(1, n). That stops at n - 1 and gives the wrong answer. Use range(1, n + 1) to include n.
  • Forgetting to set total to 0 before the loop.
  • Writing the formula as n * n + 1 // 2. Order of operations matters: the parentheses around (n + 1) are needed.

Done?

You can now repeat work with every kind of loop. Next, Nested loops nests loops to build grids, and Loop patterns names the jobs loops do most. Then Part 4's mini-projects — a Number Guessing Game and Rock-Paper-Scissors — combine decisions and repetition.