A descending number triangle prints digits 1..i on each row, with the outer loop counting down so the first row is longest.
Rule: for i = n..1, print 1..i
12345
1234
123
12
1 ← 5 rowsIn Python you solve it with two nested for loops: the outer loop picks the row length, the inner loop prints digits with print(j, end=""), then bare print() ends the row. Flip the outer loop upward for an ascending triangle (Program 5).
Outer loop counts down from rows to 1. Inner loop prints digits 1..i. End each row with print().
| Method | Idea | Best for |
|---|---|---|
| Nested loops | Outer = length n..1, inner = digits 1..i via print(..., end="") | Learning, interviews, exams |
| Spaced digits | print(j, end=" ") instead of print(j, end="") | Easier reading on each row |
for i from rows down to 1:
for j from 1 to i:
print j (no newline)
print newline| Goal | Pattern |
|---|---|
| Shrink each row | for i in range(rows, 0, -1): |
Print digits 1..i | for j in range(1, i + 1): print(j, end="") |
| End the row | print() |
| Spaced form | print(j, end=" ") |
| Ascending instead | for i in range(1, rows + 1): with the same inner loop |
| API | Effect | Use for |
|---|---|---|
print(j, end="") | Stays on the same line | Each digit j |
print() | Ends the current line | After the inner loop |
Print all digits without a newline, then end the row once.
Change the row count and the descending triangle updates instantly — capped at 9 so every digit stays a single character.
Trace rows = 4 — each outer-loop value of i and the digits the inner loop prints.
i | Inner j | Printed row | Digits |
|---|---|---|---|
4 | 1..4 | 1234 | 4 |
3 | 1..3 | 123 | 3 |
2 | 1..2 | 12 | 2 |
1 | 1..1 | 1 | 1 |
Total digits are 4+3+2+1 = 10 — the triangular number n(n+1)/2.
Three complete programs: fixed height, input(), and a spaced-digit variant. Use View Output for sample results.
rows = 5Outer loop shrinks the length; inner loop prints digits 1..i.
rows = 5
for i in range(rows, 0, -1):
for j in range(1, i + 1):
print(j, end="")
print()1. Shrink the count. for i in range(rows, 0, -1) yields 5, 4, 3, 2, 1.
2. Print digits. When i = 5, the inner loop prints 12345; when i = 1, just 1.
3. Newline. Bare print() after the inner loop starts the next shorter row.
Read the row count from the keyboard. Prefer a try / except in real apps (shown in the tip below).
rows = int(input("Enter the number of rows: "))
for i in range(rows, 0, -1):
for j in range(1, i + 1):
print(j, end="")
print()1. Read rows. input() returns a string; int(...) converts it to a whole number.
2. Same nested loops. Four rows start at 1234 and end at 1.
3. Safer input tip. Bare int(input()) raises ValueError on letters. Prefer:
raw = input("Enter the number of rows: ").strip()
try:
rows = int(raw)
except ValueError:
print("Enter a positive whole number.")
raise SystemExit(1)
if rows < 1:
print("Enter a positive whole number.")
raise SystemExit(1)Same loops with a trailing space so digits are easier to read.
rows = 5
for i in range(rows, 0, -1):
for j in range(1, i + 1):
print(j, end=" ")
print()1. Same structure. Only the print call changes — loops stay identical to Example 1.
2. Space after each digit. print(j, end=" ") separates values for clearer scanning.
3. When to use it. Prefer the tight form for classic screenshots; use spaced form when teaching or tracing by hand.
Check these before calling the solution done.
for i in range(1, rows + 1)That outer loop grows the triangle (1, 12, 123…). Keep range(rows, 0, -1) for this pattern.
print(j) inside the inner loopThat puts each digit on its own line. Use print(j, end="") for digits; call bare print() only after the row finishes.
range(1, i) instead of range(1, i + 1)You drop the last digit on every row (e.g. 1234 becomes 123).
Output is just 1 — a good sanity check.
The outer loop never runs. Validate and prompt again for clearer UX.
ValueErrorint(input()) throws on letters — prefer try / except ValueError.
| Program | Time | Extra space |
|---|---|---|
| Fixed / input (Examples 1–2) | O(n²) | O(1) |
| Spaced digits (Example 3) | O(n²) | O(1) |
There are n rows printing n+(n-1)+…+1 digits, so total work is n(n+1)/2.
i = n..1, print digits 1..i with print(j, end="").range(rows, 0, -1) so the first line is longest.print() advances after each row.One line: for each length from n down to 1, print 1..i with end="", then call print().
Row i prints digits 1 through i. The outer loop counts down from rows, so the first line is longest and each row shortens by one digit — still O(n²) total prints. This is the classic first console pattern in Python labs.
Keep a descending width, but shift the starting digit on each row.
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