Multiplying With Only Addition: From Loops to a Smaller Copy

How can 5×4 become 5 + 5×3 — and why does that one rewrite of the same problem make the loop disappear entirely?

Finger exercises

Short drills on what this video just taught. Write the code, run the checks, and reveal the answer only if you are stuck.

0 / 5 passed

Exercise 1 of 5

Trace the countdown loop

Here is the while-loop version of multiplication from the video:

def mult_iter(a, b):
    result = 0
    while b > 0:
        result += a
        b -= 1
    return result

Run mult_iter(7, 3) in your head. Every time the loop body finishes, result is holding a new value. Assign to trace a list of those values, in the order they appear — one entry per completed pass, and do not include the starting 0.

# What result holds after each pass of mult_iter(7, 3).
trace = ...  # your code here — a list of the values, in order

# What result holds after each pass of mult_iter(7, 3).
trace = ...  # your code here — a list of the values, in order

Python runs in your browser

⌘/Ctrl + Enter runs

is a list

has one entry per completed pass

matches the running total after each pass

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