Python Number Pattern (Decreasing then Increasing)

Beginner
5 min read
Updated: Sep 2026
3 programs
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Mixed number triangle pattern in Python programming (12345, 21234, 32123, 43212, 54321)
Definition

What Is This Pattern?

A mixed number triangle builds each row from two halves: descending i..2, then ascending 1..(rows - i + 1). Every row has exactly rows digits — with rows = 5 you get 12345, 21234, 32123, 43212, 54321.

Remember
Rule: print i..2, then 1..(rows-i+1)

12345
21234
32123
43212
54321     ← rows = 5

Unlike Program 49 (products i*j), this shape concatenates digit sequences — no multiplication.

Approach

How to Solve It

Outer loop picks row i. Two inner loops fill the descending half, then the ascending half.

MethodIdeaBest for
Two inner loopsDescending j = i..2, then ascending k = 1..(rows-i+1)Learning, interviews, demos
Compact traceSame logic with rows = 3Quick dry-runs on paper

Pseudocode

Pseudocode
for i from 1 to rows:
    for j from i down to 2:
        print j (no newline)
    for k from 1 to (rows - i + 1):
        print k (no newline)
    print newline

Cheat sheet

GoalPattern
Outer rowsfor i in range(1, rows + 1):
Descending halffor j in range(i, 1, -1): print(j, end="")
Ascending halffor k in range(1, rows + 2 - i): print(k, end="")
End the rowprint()
Digits per rowAlways rows

Printing Numbers vs Starting a New Line

APIEffectUse for
print(j, end="") / print(k, end="")Stays on the same lineEach digit
print()Ends the current lineAfter both inner loops

Print digits without a newline, then end the row once. Putting bare print() inside either inner loop turns the pattern into a vertical list.

Try it

Live Preview

Change the row count and the mixed triangle updates instantly.

Use rows from 1 to 9 (single digits stay tidy). Tap a chip or type a value — the preview redraws as you go.

Live result 5 rows · 25 digits
12345
21234
32123
43212
54321
Trace

Worked Walkthrough

Trace row i = 3 with rows = 5 — descending then ascending.

HalfLoopPrintsLine so far
Descendingj = 3, 23, 232
Ascendingk = 1..(5-3+1) = 1..31, 2, 332123

When i = 1, the descending loop never runs — the whole row is just 1..rows. When i = rows, the ascending loop prints only 1, so the row is rows..(2)1.

Code

Python Programs

Three complete programs: fixed rows = 5, input() rows, and a compact rows = 3 demo. Use View Output to reveal sample results.

Example 1 — Fixed rows = 5

Hard-coded height — descending half, then ascending half, on every row.

Python
rows = 5

for i in range(1, rows + 1):
    for j in range(i, 1, -1):
        print(j, end="")
    for k in range(1, rows + 2 - i):
        print(k, end="")
    print()

How It Works

1. Outer loop picks the row. i runs from 1 to 5 — one full line per value.

2. Descending half first. range(i, 1, -1) prints i..2 (skipped when i = 1).

3. Ascending half fills the rest. k runs from 1 to rows + 1 - i, then bare print() ends the row.

Example 2 — User Input Rows

Read the row count at runtime — both halves scale automatically.

Python
try:
    rows = int(input("Enter the number of rows: "))
except ValueError:
    print("Please enter a positive integer.")
    raise SystemExit(1)

if rows < 1:
    print("Please enter a positive integer.")
    raise SystemExit(1)

for i in range(1, rows + 1):
    for j in range(i, 1, -1):
        print(j, end="")
    for k in range(1, rows + 2 - i):
        print(k, end="")
    print()

How It Works

1. Same two-loop core. Only the source of rows changes from a literal to input().

2. Width follows rows. Entering 4 yields four digits on every line.

3. Safer input tip. Cap demos for readable output:

Safer input tip
if rows < 1 or rows > 9:
    print("Enter a whole number from 1 to 9.")
    raise SystemExit(1)

Example 3 — Compact rows = 3

Smaller height for quick tracing on paper or in interviews.

Python
rows = 3

for i in range(1, rows + 1):
    for j in range(i, 1, -1):
        print(j, end="")
    for k in range(1, rows + 2 - i):
        print(k, end="")
    print()

How It Works

1. Only three rows. Easy to dry-run every descending and ascending step by hand.

2. Same formula. Nothing changes except rows — proving the pattern scales.

3. Last row is fully descending. Row 3 prints 321 — 3 2 then 1.

Edge Cases & Pitfalls

Check these before calling the solution done.

Descending bound

Stop at 2, not at 1

Use range(i, 1, -1). Going down to 1 duplicates the leading 1 from the ascending half.

Ascending length

Use rows + 1 - i

Wrong bounds break the fixed width of rows digits per line. In Python that is range(1, rows + 2 - i).

Newline

Do not put print() inside either inner loop

Call bare print() only after both halves finish.

Between loops

No break between halves

Run both inner loops back-to-back. A newline between them splits each row in half.

rows = 1

Single value

Output is just 1. A good sanity check for input validation.

input()

Catch ValueError

Bare int(input()) crashes on non-numeric text — wrap it in try/except ValueError.

Analysis

Time and Space Complexity

ProgramTimeExtra space
Nested loops (Examples 1–3)O(n²)O(1)

Each of n rows prints exactly n digits, so total work is n². Only a few integers of extra memory.

Remember

Key Takeaways

  • Rule: print i..2, then 1..(rows - i + 1).
  • Fixed width: every row has exactly rows digits.
  • Break the row: call bare print() only after both inner loops.
  • Complexity: O(n²) time; O(1) extra space.

One line: for each row i, print descending i..2 then ascending 1..(rows-i+1), then end the line.

Frequently Asked Questions

Each row prints two parts: first a descending sequence from i down to 2, then an ascending sequence from 1 up to (rows - i + 1). Row 2 becomes 2 + 1234 = 21234.
One inner loop prints the descending part (j = i down to > 1). The other prints the ascending part (k = 1..(rows-i+1)). Splitting them keeps the two halves clear.
When i = 1, the descending loop j = i; j > 1 never runs. Only the ascending loop prints 1..rows.
Program 49 prints i*j products on each row. Program 50 concatenates digit sequences — descending then ascending — with no multiplication.
Printing a digit with end="" stays on the same line. Bare print() ends the current row. Digits use end=""; the row break uses print() after both inner loops.
O(n²) for n rows because each row prints n digits and there are n rows.
for j in range(i, 1, -1) prints i..2 — the same as a countdown that stops before 1.
Use try/except ValueError around int(input()) and require rows >= 1 — see Example 2.

Did you know?

Each row combines two sequences: descending i..2, then ascending 1..(rows-i+1). Every row has exactly rows digits — total prints = n², time O(n²).

Next: Alternating Ascending/Descending Triangle

Continue with the next pattern in the Python number-pattern series.

Program 51 tutorial →

About the author

Mari Selvan M P
Mari Selvan M P 🔗

Developer, cloud engineer, and technical writer

  • Experience 12 years building web and cloud systems
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I write practical tutorials so students and working developers can learn by doing—from databases and APIs to deployment on AWS.

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Python Number Pattern 49 — Multiplication Triangle Python Number Pattern 51 — Alternating Ascending/Descending Triangle