Produce a filtered list of products from a Cartesian product with a condition.

To express a concise, filtered transformation of a Cartesian product for further processing.

When needing to generate combinations of numbers that satisfy a specific arithmetic condition, e.g., combinatorial filtering or test data generation.

Used in list comprehensions for data generation, algorithmic puzzles, or teaching nested iteration with conditions.

[expression for var1 in iterable1 for var2 in iterable2 if condition]

[x*y for x in range(1,6) for y in range(1,6) if x != y and (x+y) % 3 == 0]

expression iterable1 iterable2 condition

• range for in if and %

• expression: x+y
• x-y
• iterable: range(1
• n)
• list
• condition: x==y
• (x+y)%2==0

Placing the condition incorrectly (e.g., before the iterables), forgetting to exclude x==y, using wrong modulus value

[x*y for x in range(1,6) for y in range(1,6)] (no filter), [x*y for x in range(1,6) for y in range(1,6) if x == y] (only equal pairs)

Confusing the placement of 'if' clause, mixing 'and'/'or' logic, misjudging the range bounds

• list comprehension patterns

The condition ensures distinct pairs whose sum is a multiple of three, yielding products like 2, 3, 4, 6, 8, 9, 10, 12, 15, 16, 18, 20.

Produces a concise, filtered Cartesian product ready for further consumption (e.g., summation, iteration).

Think of distinct pairs from 1‑5 whose sums are multiples of three, then multiply them.

The first 'for' clause defines the outer loop; swapping them changes the order of generated pairs.

Use generator expressions for lazy evaluation: (x*y for x in range(1,6) for y in range(1,6) if x != y and (x+y) % 3 == 0)