An odd-length descending number triangle prints ascending digits 1..i, but only for odd row widths — so you see 1234567, 12345, 123, 1.
Rule: for i = max..1 step -2, print 1..i
1234567
12345
123
1 ← max = 7In Python you solve it with an outer loop that steps by 2: for i in range(max_n, 0, -2), an inner loop that prints each digit with print(j, end=""), then bare print() ends the row. Program 13 flips direction with i % 2; this pattern always ascends but skips even widths.
Outer loop counts down from an odd max_n with step 2. Inner loop prints 1..i. End each row with print().
| Method | Idea | Best for |
|---|---|---|
| Step by 2 | Outer range(..., -2) visits only odd widths | Learning, interviews, exams |
| Every width | Same inner loop with range(..., -1) for comparison | Seeing what the custom step skips |
for i from max down to 1 step 2:
for j from 1 to i:
print j (no newline)
print newline| Goal | Pattern |
|---|---|
| Walk odd widths | for i in range(max_n, 0, -2): |
Print 1..i | for j in range(1, i + 1): print(j, end="") |
| End the row | print() |
| Force odd max | if max_n % 2 == 0: max_n -= 1 |
| Every width (compare) | for i in range(max_n, 0, -1): |
| API | Effect | Use for |
|---|---|---|
print(j, end="") | Stays on the same line | Each digit in 1..i |
print() | Ends the current line | After the inner loop |
Print all digits without a newline, then end the row once.
Change the maximum width and the odd-length triangle updates instantly — prefer odd values so the top row matches the classic demo.
Trace max_n = 7 — each outer-loop value of i, the inner range, and the printed row.
i | Inner j | Length | Printed row |
|---|---|---|---|
7 | 1..7 | 7 | 1234567 |
5 | 1..5 | 5 | 12345 |
3 | 1..3 | 3 | 123 |
1 | 1..1 | 1 | 1 |
Total digits are 7+5+3+1 = 16 — for odd max n, that equals ((n+1)/2)².
Three complete programs: fixed odd max, input(), and an every-width comparison. Use View Output for sample results.
max_n = 7Hard-coded odd maximum — outer steps by 2, inner prints 1..i.
max_n = 7
for i in range(max_n, 0, -2):
for j in range(1, i + 1):
print(j, end="")
print()1. Outer skips even widths. range(max_n, 0, -2) visits 7, 5, 3, 1 only.
2. Inner prints ascending digits. j runs from 1 to i with print(j, end="").
3. End the row. Call bare print() only after the inner loop finishes.
Read the maximum width from the keyboard. Prefer an odd value so the top row matches the classic demo.
max_n = int(input("Enter an odd maximum (e.g. 9): "))
for i in range(max_n, 0, -2):
for j in range(1, i + 1):
print(j, end="")
print()1. Same loop core. Only the source of max_n changes from a literal to keyboard input.
2. Entering 5 stops early. You get three odd-length rows ending at 1.
3. Safer input tip. Validate and force an odd top width:
raw = input("Enter an odd maximum (e.g. 9): ").strip()
try:
max_n = int(raw)
except ValueError:
print("Enter a positive whole number.")
raise SystemExit(1)
if max_n < 1:
print("Enter a positive whole number.")
raise SystemExit(1)
if max_n % 2 == 0:
max_n -= 1range(..., -1))Same inner loop with a normal step — includes even lengths for comparison.
max_n = 7
for i in range(max_n, 0, -1):
for j in range(1, i + 1):
print(j, end="")
print()1. Only the step changed. range(..., -1) visits every width; range(..., -2) in Example 1 skips the even ones.
2. Same inner rule. Digits still print 1..i with print(j, end="").
3. Compare side by side. Seeing both outputs makes the custom step easy to remember.
Check these before calling the solution done.
An even start prints even lengths (6, 4, 2). Force odd with if max_n % 2 == 0: max_n -= 1.
range(..., -2), not -1range(..., -1) reprints the every-width triangle (see Example 3).
print(i, end="") instead of print(j, end="")That repeats the row length. This pattern prints the sequence value of j.
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.
Output is just 1 — a good sanity check.
The outer loop never runs. Validate and prompt again for clearer UX.
| Program | Time | Extra space |
|---|---|---|
| Odd widths (Examples 1–2) | O(n²) | O(1) |
| Every width (Example 3) | O(n²) | O(1) |
For odd max n you print 1+3+…+n digits — about half of the full triangle, but still O(n²).
i from max_n down by 2, print digits 1..i.range(..., -2) is what skips even row lengths.print() advances after each row.0 and 1.One line: step i down by 2 from an odd max, print 1..i with end="", then call print().
Only odd-length rows print. The outer loop uses range(..., -2) (7, 5, 3, 1) and the inner loop prints 1..i — still O(n²) total digit prints for maximum width n.
Continue with rows built from alternating 0 and 1.
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