Rotating Number Pattern in Python

Beginner

⏱️ 9 min read

📚 Updated: Sep 2026

🎯 3 Code Examples

🚀 Live Preview

Nested Loops

Rotating number pattern output in Python (12345, 21234, 32123, 43212, 54321)

Overview

What You’ll Learn

Program 50 prints a mixed number triangle: each row combines descending i..2 with ascending 1..(rows-i+1) — a natural step after Program 49’s multiplication triangle. This tutorial covers two inner loops per row, a live preview, worked Python examples, edge cases, and complexity.

Shape Rule

Two halves per row

Row i prints descending i..2, then ascending 1..(rows-i+1) — always rows digits total.

Outer Loop

i = 1..rows

for i in range(1, n + 1): picks the current row index.

Descending Loop

j = i..2

for j in range(i, 1, -1): prints the descending half (skipped when i = 1).

Ascending Loop

k = 1..(rows-i+1)

for k in range(1, n + 2 - i): prints the ascending half on each row.

Live Preview

rows = 3..9

Pick row count and draw the mixed number triangle in the browser.

O(n²)

Complexity

Total prints = n×n = n² — each row has exactly n digits.

Introduction

A mixed number triangle pattern prints row i with i products: print descending i..2, then ascending 1..(rows-i+1). With rows = 5, you get 12345, 21234, 32123, 43212, 54321.

In Python, nested loops handle this: outer i = 1..n, inner descending j = i..2, inner ascending k = 1..(n-i+1), then print().

Why it matters?

It bridges Program 49’s multiplication triangle to patterns with two inner loops per row — combining descending and ascending digit sequences.

Key Highlights

Descending half

j runs i..2.

Ascending half

k runs 1..(rows-i+1).

vs Program 49

Program 49 prints i*j products; Program 50 concatenates digit sequences.

Series Foundation

Follow Program 49; continue to Program 51 next.

In short: outer i = 1..rows, inner descending j = i..2, inner ascending k = 1..(rows-i+1), then print().

Foundation

📝 Problem & Approach

Given row count rows = 5, print a mixed number triangle — row i shows descending i..2 then ascending 1..(rows-i+1).

Python

# n = 5
//12345
//21234
//32123
//43212
//54321

Inputs & Outputs

Item	Type	Description
`rows`	int	How many triangle rows to print.
`i` (outer)	int	Current row index — runs from `1` to `rows`.
`j` (descending)	int	Prints `i..2` — skipped when `i = 1`.
`k` (ascending)	int	Prints `1..(rows-i+1)` on each row.
Row length	int	Always `rows` digits per row.

Minimal workflow

Pseudocode

for i from 1 to rows:
    for j from i down to 2:
        print j
    for k from 1 to (rows - i + 1):
        print k
    print newline

Approach comparison

Approach	Idea	Best for
Two inner loops	Descending `j = i..2`, ascending `k = 1..(rows-i+1)`	Learning and interviews
User-input rows	`n = int(input())`	Flexible row count
Compact trace	`rows = 3` on paper first	Quick dry-runs before full demo
Spaced variant	`print(j, end=" ")`	Easier reading per row

Cheat Sheet

⚡ Quick Reference

Goal	Pattern
Outer loop	`for i in range(1, n + 1):`
Descending half	`for j in range(i, 1, -1): print(j, end="");`
Ascending half	`for k in range(1, n + 2 - i): print(k, end="");`
End row	`print();`
Row 1 special case	Descending loop skipped — only ascending prints
Program 49 contrast	Program 49 prints i*j products; Program 50 uses digit sequences

Compare

📋 Fixed Rows vs User Input vs Compact Trace

Same triangle — three ways to set row count and format output.

Fixed rows

rows = 5

Hard-coded height for demos

User input

int(input())

Read row count with user input

Compact trace

rows = 3

Quick dry-run on paper

Descending

j = i..2

First inner loop per row

Ascending

k = 1..(rows-i+1)

Second inner loop per row

Context

When This Pattern Shows Up

Reach for this pattern when teaching two inner loops per row and combining descending with ascending sequences.

Post Program 49 exercise
Natural follow-up after Program 49’s multiplication triangle — introduces two inner loops per row.
Multiplication tables
Row i is the i-times table — visual bridge to arithmetic grids.
Two halves per row
Total prints = n(n+1)/2 — classic nested-loop complexity example.
Gateway to variants
Compare Program 49 (multiplication triangle) with this mixed number triangle, then continue to Program 51.
Not a UI layout tool
This is a console teaching pattern — not how you build modern app screens.

Key benefit: one small program that locks in two inner loops per row and O(n²) thinking.

Interactive

🔮 Live Preview

Choose row count between 3 and 9 and draw the mixed number triangle in the browser.

Hands-On

Examples Gallery

Three complete Python programs — fixed n, user input, and a compact trace demo. Click View Output to reveal sample console results.

📚 Getting Started

Print five rows of the mixed number triangle with two inner loops per row.

Example 1 — Fixed `n = 5`

Hard-coded row count — descending i..2 then ascending 1..(n-i+1) on each line.

Python

n = 5

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

How It Works

When i = 2, the first loop prints 2, then the second prints 1234 — output 21234. When i = 1, the descending loop is skipped and only 12345 prints.

📈 User Input

Read row count with int(input()) and validation.

Example 2 — User Input n

Read n with int(input()) and validate the result.

Python

try:
    n = int(input("Enter n: "))
except ValueError:
    print("Please enter a positive integer.")
    raise SystemExit(1)

if n < 1:
    raise SystemExit(1)

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

How It Works

Same two-loop core as Example 1; only the source of rows changes from a literal to user input.

⚡ Compact Trace

Smaller row count for quick tracing on paper or in interviews.

Example 3 — Compact `n = 3`

Use n = 3 to trace both inner loops quickly before scaling to 5 rows.

Python

n = 3

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

How It Works

With only three rows you can trace every iteration of both inner loops on paper before running the full rows = 5 demo.

🧠 How the Algorithm Prints Rows

Choose row count

No imports needed. Set n = 5 or read from user input — controls pattern height.

Setup

Outer loop — row index

for i in range(1, n + 1): — selects which row to print.

Outer

Two inner loops

for j in range(i, 1, -1): prints descending digits, then for k in range(1, n + 2 - i): prints ascending digits.

Inner

New line per row

print() after both inner loops finish each row.

Break

Mixed number triangle complete

Total prints = n×n = n² — O(n²) time, O(1) extra memory.

Trace

🔎 Worked Walkthrough — `rows = 5`

Trace each row’s descending and ascending halves and the full line output.

`i`	Descending (`j`)	Ascending (`k`)	Row output
`1`	(skip)	`1..5`	`12345`
`2`	`2`	`1..4`	`21234`
`3`	`3,2`	`1..3`	`32123`
`4`	`4,3,2`	`1..2`	`43212`
`5`	`5,4,3,2`	`1`	`54321`

Each row prints exactly rows digits — descending count plus ascending count always equals rows.

Use Cases

Where this tiny pattern (and its loop structure) shows up beyond the homework prompt.

1. Teaching Nested Loops

Inner bound grows with outer index — classic nested-loop exercise.

Example: trace row i = 4 in the walkthrough table.

2. Multiplication Tables

Row i is the i-times table — visual arithmetic bridge.

Example: row 5 ends with 54321 — descending 5432 plus ascending 1.

3. Output Formatting Drills

Practice print(j, end="") vs print() with two inner loops per row.

Example: put print() inside either inner loop by mistake.

4. Two Halves Per Row

Total prints = n(n+1)/2 — links loops to summation formulas.

Example: 10 rows print 55 values total.

5. Complexity Intuition

Growing inner bound makes O(n²) concrete — count prints for n rows.

Example: 5 rows = 1+2+3+4+5 = 15 prints.

6. Input Validation Labs

Pair the pattern with try/except ValueError and positive-row checks.

Example: reject rows <= 0 and re-prompt.

Pro Tip: when an interviewer asks for patterns, explain outer/inner roles first — then write the loops. The story matters as much as the code.

Advantages

Why this pattern earns a permanent spot in beginner Python courses.

1. Instant Visual Feedback
Wrong inner bounds show up immediately as a broken triangle.
2. Real Math Connection
Each row combines descending and ascending halves — not abstract loop drill.
3. Easy to Extend
Change rows, use fixed-width format, or switch to full rectangular table.
4. O(1) Extra Memory
Streaming output needs no storage beyond loop counters.

Pro Tip: trace row i = 4 on paper — watch how inner j runs from 1 to 4 producing 4, 8, 12, 16.

Usage Tips

Small habits that keep number-pattern code clean.

1. Two Inner Loops
Descending j = i..2, then ascending k = 1..(rows-i+1) — each row always has rows digits.
2. Call try/except ValueError
Avoid crashes when the user types letters instead of a number.
3. Newline After Both Loops
Only call print() after both inner loops finish the row.
4. Fixed-Width Formatting
Trace rows = 3 on paper before coding the full rows = 5 demo.
5. Dry-Run rows = 5
Trace five rows on paper before coding the full 10-row demo.

Pro Tip: if the output is a vertical list of single numbers, you almost certainly put print() inside one of the inner loops.

Common Pitfalls

Mistakes that commonly break mixed number triangle patterns.

1. Newline Inside Inner Loop
Each digit lands on its own line — you get a column, not a mixed triangle row.
→ Use print(j, end="") and print(k, end="") without spaces; print() only after both inner loops.
2. Wrong Inner Bound
Using j <= rows every row makes a full rectangle, not a triangle.
→ Use for j in range(i, 1, -1): for descending, then for k in range(1, n + 2 - i): for ascending.
3. Swapping i and j in Product
j > 1 skips when i = 1, but order matters in other patterns — stay consistent.
→ Use j > 1 (not j >= 1) so row 1 skips the descending loop correctly.
4. Forgetting Newline After Row
All digits print on one long line without row breaks.
→ Add print() after both inner loops complete.
5. Bare int(input())
Letters or empty input raise ValueError with bare int(input()).
→ Catch ValueError and re-prompt on failure.

Edge Cases

Check these inputs before calling the solution done.

rows = 1

Single row

Output is just 1 on one line.

rows = 0

Empty output

Outer loop never runs — print nothing or show a message.

Negative

`rows < 0`

Treat as invalid; re-prompt instead of silent empty output.

rows = 5

Compact trace

Five rows ending with 54321 — good for dry-runs.

Bad input

Non-numeric input

Bare int(input()) raises ValueError — use try/except first.

Large rows

Wide output

Row 9 has 9 digits — output grows as n² total prints.

Drill

🎯 Practice Problems

Try these variations to lock in the pattern.

1. Compare with Program 49

Program 49 prints i*j products on each row
Program 50 uses two inner loops with digit sequences

2. Change rows

Try rows = 4 or rows = 8 in the live preview
Same nested loops, different triangle size

3. Next in series

Continue with Program 51
Build on mixed number patterns

4. Spaced output

Add spaces with print(j, end=" ")
Same loops, wider visual spacing

Important

Notes

Two inner loops. Outer: i = 1..rows. Descending: j = i..2. Ascending: k = 1..(rows-i+1).
print(j, end="") stays on the line; print() advances — call it only after both inner loops finish.
Validate rows > 0 for interactive programs; rows = 1 prints a single 1.
Total prints = n×n = n² for n rows — each row has exactly n digits.

Quick Takeaway: outer i = 1..rows, inner descending j = i..2, inner ascending k = 1..(rows-i+1), then print().

Analysis

⏱️ Time and Space Complexity

Program	Time	Extra space
Nested loops (Examples 1–3)	`O(n²)`	`O(1)`
Total prints for n rows	`n(n+1)/2` values	`n²` (n digits × n rows)

Wrap Up

🎉 Conclusion

The mixed number triangle is a natural follow-up to Program 49: two inner loops per row combining descending and ascending digit sequences. Master the fixed-rows version, then try user input and the compact 3-row trace.

Practice the three examples above, then continue to Program 51 for the next pattern in the series.

Row i prints descending i..2 then ascending 1..(rows-i+1) — always rows digits total.

View Examples Gallery Continue to Program 51

Pro Tips

💡 Best Practices

✅ Do

Outer: for i in range(1, n + 1):
Descending: for j in range(i, 1, -1): print(j, end="");
Ascending: for k in range(1, n + 2 - i): print(k, end="");
Call print() after both inner loops
Validate rows > 0 for interactive programs

❌ Don’t

Call print() inside either inner loop
Use j >= 1 in descending loop when you meant j > 1
Forget the row break after both inner loops
Ignore bad input in user-facing demos
Skip the rows = 3 dry-run before coding rows = 5

Summary

Key Takeaways

Knowledge Unlocked

Five things to remember about this mixed number triangle

Print the pattern the beginner-friendly way.

Core concepts

△ 01

Rule

Row i: i..2 then 1..(rows-i+1)

Definition

↻ 02

Outer loop

i = 1..rows

Code

↓ 03

Inner loop

j = i..2, k = 1..(rows-i+1)

Code

↵ 04

Row length

Always rows digits

Logic

O 05

Complexity

O(n²) time

Analysis

❓ Frequently Asked Questions

How does each row form in this rotating pattern?

Each row prints two parts: first a descending sequence from i down to 2, then an ascending sequence from 1 up to (n - i + 1). Row 2 becomes 2 + 1234 = 21234.

Why do we use two inner loops?

One inner loop prints the descending part (j = i down to > 1). The other prints the ascending part (k = 1..(n-i+1)). Splitting them keeps the two halves clear.

Why does row 1 print 12345 with no leading digit?

When i = 1, the descending loop j = i; j > 1 never runs. Only the ascending loop prints 1..n — a full ascending line.

Why does the second row start with 2 (21234)?

The descending loop prints i first. For i = 2, that is 2. Then the ascending loop prints 1..(n-2+1) = 1..4, giving 21234.

How can I change the size of the pattern?

Change n or read it from user input with int(input()) — see Example 2.

What is the time complexity?

O(n²) for n rows because each row prints n digits and there are n rows — total prints = n × n = n².

How is this different from Program 49?

Program 49 prints i*j products on each row. Program 50 concatenates digit sequences — descending then ascending — with no multiplication.

Should I use j >= 2 or j > 1?

Both work for the descending loop: for j in range(i, 1, -1) and range(i, 0, -1) with j > 1 check print the same i..2 sequence.

How should I read n safely?

Use try/except ValueError around int(input()). Bare int(input()) raises ValueError on bad input.

What happens when n is 1?

One row prints 1 — the descending loop is skipped and the ascending loop prints only 1.

Did you Know? 🔊

Each row combines two sequences: descending i..2, then ascending 1..(n-i+1). Row 2 prints 21234; row 5 prints 54321 — still O(n²) total prints for n rows.

Continue to Program 51

Move on to the next pattern in the Python number-pattern series.

Program 51 tutorial →

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Python Number Pattern 49 — Multiplication Triangle Python Number Pattern 51

Rotating Number Pattern in Python

What You’ll Learn

Shape Rule

Outer Loop

Descending Loop

Ascending Loop

Live Preview

O(n²)

Introduction

Why it matters?

Descending half

Ascending half

vs Program 49

Series Foundation

📝 Problem & Approach

Inputs & Outputs

Minimal workflow

Approach comparison

⚡ Quick Reference

📋 Fixed Rows vs User Input vs Compact Trace

When This Pattern Shows Up

Post Program 49 exercise

Multiplication tables

Two halves per row

Gateway to variants

Not a UI layout tool

🔮 Live Preview

Examples Gallery

📚 Getting Started

Example 1 — Fixed n = 5

How It Works

📈 User Input

Example 2 — User Input n

How It Works

⚡ Compact Trace

Example 3 — Compact n = 3

How It Works

🧠 How the Algorithm Prints Rows

Choose row count

Outer loop — row index

Two inner loops

New line per row

Mixed number triangle complete

🔎 Worked Walkthrough — rows = 5

Use Cases

1. Teaching Nested Loops

2. Multiplication Tables

3. Output Formatting Drills

4. Two Halves Per Row

5. Complexity Intuition

6. Input Validation Labs

Advantages

1. Instant Visual Feedback

2. Real Math Connection

3. Easy to Extend

4. O(1) Extra Memory

Usage Tips

1. Two Inner Loops

2. Call try/except ValueError

3. Newline After Both Loops

4. Fixed-Width Formatting

5. Dry-Run rows = 5

Common Pitfalls

1. Newline Inside Inner Loop

2. Wrong Inner Bound

3. Swapping i and j in Product

4. Forgetting Newline After Row

5. Bare int(input())

Edge Cases

Single row

Empty output

rows < 0

Compact trace

Non-numeric input

Wide output

🎯 Practice Problems

1. Compare with Program 49

2. Change rows

3. Next in series

4. Spaced output

Example 1 — Fixed `n = 5`

Example 3 — Compact `n = 3`

🔎 Worked Walkthrough — `rows = 5`

2. Call `try/except ValueError`

5. Bare `int(input())`

`rows < 0`