A triangular multiplication pattern prints the products i×1, i×2, … up to i×i on each row.
Rule: on row i, print i*j for j = 1..i
1
2 4
3 6 9
4 8 12 16
5 10 15 20 25 ← rows = 5Follows the powers of 11 in Program 48; next is the rotating number pattern in Program 50.
One nested loop: outer picks the row base i, inner prints the first i multiples.
| Method | Idea | Best for |
|---|---|---|
| Space-separated | Print i * j for j = 1..i | Learning, interviews, exams |
| Fixed width | Same products with f"{i * j:3d}" | Neater columns |
for i from 1 to rows:
for j from 1 to i:
print i * j and a space
print newline| Goal | Pattern |
|---|---|
| Walk rows | for i in range(1, rows + 1): |
| Walk columns | for j in range(1, i + 1): |
| Print product | print(i * j, end=" ") |
| Align columns | print(f"{i * j:3d}", end="") |
| End the row | print() |
| API | Effect | Use for |
|---|---|---|
print(i * j, end=" ") | Stays on the same line | Each product plus a trailing space |
print() | Ends the current line | After the column loop finishes a row |
Print products without a newline, then end the row once.
Change the row count and the multiplication triangle updates instantly.
rows = 4Trace each row’s products from i*1 through i*i.
i | Products i*j | Printed row |
|---|---|---|
1 | 1 | 1 |
2 | 2, 4 | 2 4 |
3 | 3, 6, 9 | 3 6 9 |
4 | 4, 8, 12, 16 | 4 8 12 16 |
Total products for n rows = n(n+1)/2. Last value on row i is always i*i.
Three complete programs: fixed 5 rows, input() rows, and fixed-width columns. Use View Output for sample results.
rows = 5Nested loops print i * j with a trailing space.
for i in range(1, 6):
for j in range(1, i + 1):
print(i * j, end=" ")
print()1. Outer loop. i is the row multiplier — row 3 uses 3 as the base.
2. Inner loop. j runs from 1 to i; each cell prints i * j.
3. Newline. Bare print() after the inner loop starts the next row.
Read the row count with input() and build the same triangle.
try:
rows = int(input("Enter number of rows: "))
except ValueError:
print("Please enter a positive whole number.")
raise SystemExit(1)
if rows < 1:
print("Please enter a positive whole number.")
raise SystemExit(1)
for i in range(1, rows + 1):
for j in range(1, i + 1):
print(i * j, end=" ")
print()1. Validate rows. Catch ValueError; require rows >= 1.
2. Same triangle. Only the bound changes from the literal 5 to the user value.
3. Safer input tip. Cap demos for readable output:
if rows < 1 or rows > 10:
print("Enter a whole number from 1 to 10.")
raise SystemExit(1)Use :3d so single- and double-digit products stay aligned.
for i in range(1, 6):
for j in range(1, i + 1):
print(f"{i * j:3d}", end="")
print()1. Same products. Still i * j for j = 1..i.
2. Width 3. f"{i * j:3d}" reserves three columns per number so digits line up.
Check these before calling the solution done.
rowsThat prints a full rectangle (multiplication table). Keep j <= i for the triangle.
j * i instead of i * jSame products — fine. Just stay consistent; both equal i * j.
print() inside the inner loopThat puts every product on its own line. Call bare print() only after the column loop.
Output is just 1 — one product on one line.
end=" "Default print(i * j) puts each product on its own line. Use end=" " (or fixed width) inside the row.
ValueErrorBare int(input()) crashes on non-numeric text — wrap it in try/except ValueError.
| Program | Time | Extra space |
|---|---|---|
| Fixed / aligned (Examples 1, 3) | O(n²) | O(1) |
| User input (Example 2) | O(n²) | O(1) |
Total printed products are 1 + 2 + … + n = n(n+1)/2, so work is quadratic in the row count.
i, print i*j for j = 1..i; last value is i*i.i; total prints = n(n+1)/2.print() advances after each row.O(n²) time; O(1) extra space.One line: for each row i, print the first i multiples of i.
On row i, print i products: i*1, i*2, … up to i*i. Total prints = n(n+1)/2 — a triangular number, so time is O(n²).
Print rows that shift or rotate their digit sequences across lines.
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