Shape Rule
digit i repeats rows-i+1 times
Row rows prints one rows, then digit rows-1 twice, and so on until 1 repeats rows times.

The descending repeating number triangle flips Program 9’s outer loop: digit decreases each row while repeats increase — nested loops, cout vs newline, and a clear visual result. This tutorial covers the shape rule, loop structure, a live preview, algorithm steps, worked C++ examples, edge cases, and complexity.
digit i repeats rows-i+1 times
Row rows prints one rows, then digit rows-1 twice, and so on until 1 repeats rows times.
Rows
for (i = rows; i >= 1; i--) picks the digit for each row, starting at rows and counting down to 1.
Digits
for (j = rows; j >= i; j--) prints digit i exactly rows - i + 1 times on that row.
Same line / next line
Repeated digits use cout << i; end each row with cout << "\n".
1–20 rows
Pick a row count and draw the descending repeating number triangle instantly in the browser.
Complexity
Total digit prints still = n(n+1)/2; extra memory stays O(1).
A descending repeating number triangle pattern starts with one copy of the top digit and adds one more repeat each line as the digit decreases. Each row prints the same digit multiple times; the repeat count grows while the digit value shrinks.
In C++ you usually solve it with two nested for loops: the outer loop picks the digit, the inner loop repeats it with cout << i, then cout << "\n" moves to the next line.
It is a natural follow-up to Program 9 in C++ courses. Once nested loops and cout click, pyramids, diamonds, and hollow shapes become much easier.
On row i, print digit i exactly rows - i + 1 times.
Outer picks the digit; inner controls how many times it repeats.
cout << i in the inner loop; cout << "\n" after.
Gateway to Program 9 (ascending repeats) and Program 11 (inverted repeats).
In short: for each row i from rows down to 1, repeat cout << i exactly rows - i + 1 times, then call cout << "\n".
Given a positive integer rows, print a descending repeating number triangle: row i repeats digit i exactly rows - i + 1 times, with the outer loop counting from rows down to 1.
// First 5 rows (conceptual shape)
// 5
// 44
// 333
// 2222
// 11111 | Item | Type | Description |
|---|---|---|
rows | int | Number of triangle lines to print (typically ≥ 1). |
| Printed output | text | Each row repeats one digit; the top row has one copy of rows, the bottom row repeats 1 for rows copies. |
for i from rows down to 1:
repeat (rows - i + 1) times:
print i (no newline)
print newline | Approach | Idea | Best for |
|---|---|---|
| Nested loops | Outer digit + inner repeats | Learning and interviews |
string(rows - i + 1, char('0' + i)) | Build the full repeated row in one call | Compact C++ style once loops are understood |
| Goal | Pattern |
|---|---|
| Walk each row | for (i = rows; i >= 1; i--) |
Repeat digit i | for (j = rows; j >= i; j--) cout << i; |
| End the row | cout << "\n"; |
| One-line row shortcut | string(rows - i + 1, char('0' + i)) repeated per row |
| Ascending variant | for (j = 1; j <= i; j++) cout << i (Program 9 ascending repeats) |
Same triangle — different ways to emit characters.
same linePrints a digit without moving to the next line
new lineEnds the current row after all digits are printed
whole rowBuilds digit i repeated rows - i + 1 times in one string
loops firstMaster nested loops before the string shortcut
Reach for this triangle when teaching or testing nested-loop basics.
Most C++ pattern series start here before pyramids and diamonds.
Outer/inner bound practice with an immediate visual check.
Combine loops with cin for a flexible row count.
Compare Program 9 (ascending repeats) and Program 11 (inverted repeats) next.
This is a console teaching pattern — not how you build modern app screens.
Key benefit: one small program that locks in nested loops, output sequencing, and O(n²) thinking.
Choose a row count between 1 and 20 and draw the descending repeating number triangle in the browser.
Three complete C++ programs — fixed row count, cin input, and a string row shortcut. Click View Output to reveal sample console results.
Print five rows of the descending repeating number triangle with nested loops.
rows = 5Hard-coded height — outer picks digit, inner controls repeat count.
#include <iostream>
using namespace std;
int main() {
int rows = 5;
int i, j;
for (i = rows; i >= 1; --i) {
for (j = rows; j >= i; --j) {
cout << i;
}
cout << "\n";
}
return 0;
} When i = 5, the inner loop runs once and prints 5. When i = 4, it prints 44, and so on until i = 1 prints 11111. cout << "\n" after the inner loop starts the next row.
Let the user choose the height at runtime.
Read the row count with cin >> rows (check cin.fail() in real apps).
#include <iostream>
using namespace std;
int main() {
int rows;
int i, j;
cout << "Enter the number of rows: ";
cin >> rows;
for (i = rows; i >= 1; --i) {
for (j = rows; j >= i; --j) {
cout << i;
}
cout << "\n";
}
return 0;
} Same nested-loop core as Example 1; only the source of rows changes. Non-numeric input sets cin’s fail bit if you ignore errors — always validate in safer labs.
Same shape using a string constructor instead of an inner digit loop.
string(rows - i + 1, char('0' + i))Build each row with string(rows - i + 1, char('0' + i)), then print with cout.
#include <iostream>
#include <string>
using namespace std;
int main() {
int rows = 5;
for (int i = rows; i >= 1; --i) {
cout << string(rows - i + 1, char('0' + i)) << "\n";
}
return 0;
} string(rows - i + 1, char('0' + i)) creates a row of repeated digit i when i is 1..9. Same shape as Example 1 without an inner digit loop — a handy C++ shortcut once the bounds make sense.
#include <iostream> brings in cout / cin. Set rows (fixed or from input).
for (i = rows; i >= 1; i--) picks the digit for the current row (5, 4, 3, …).
for (j = rows; j >= i; j--) repeats digit i with cout << i.
cout << "\n" ends the row so the next outer iteration starts fresh.
Total digit prints: 1+2+…+n = n(n+1)/2 — O(n²) time, O(1) extra memory.
rows = 4Trace each outer-loop value of i and count how many times the inner loop prints digit i.
i | Inner j range | Repeats | Printed row |
|---|---|---|---|
4 | 4..4 | 1 | 4 |
3 | 4..3 | 2 | 33 |
2 | 4..2 | 3 | 222 |
1 | 4..1 | 4 | 1111 |
Total digit prints: 1 + 2 + 3 + 4 = 10 = 4×5/2.
Where this tiny pattern (and its loop structure) shows up beyond the homework prompt.
Clearest visual proof that outer and inner bounds interact.
Example: change j <= i and watch the shape change.
Foundation for inverted, pyramid, diamond, and hollow variants.
Example: Program 9 repeats digit i exactly i times with an ascending outer loop.
Practice cout vs row newline without complex math.
Example: put cout << "\n" inside the inner loop by mistake.
Swap digits for letters, stars, or spaced output once the loop works.
Example: print i + " " for spaced repeated digits on each row.
Triangular totals make O(n²) concrete for beginners.
Example: count printed digits for n = 10 still → 55.
Pair the pattern with cin return checks and positive-row validation.
Example: reject rows <= 0 and re-prompt.
Pro Tip: when an interviewer asks for patterns, explain the outer/inner roles first — then write the loops. The story matters as much as the code.
Why this pattern earns a permanent spot in beginner C courses.
Wrong bounds show up immediately as a broken staircase.
Only loops and console output — no arrays or math libraries.
Invert, center, hollow, or change the fill character with small edits.
Streaming output needs no storage beyond loop counters.
Pro Tip: learn the nested-loop version first; treat string(rows - i + 1, char('0' + i)) as a polish shortcut afterward.
Small habits that keep number-pattern code clean.
Use rows (or n) and keep i/j for row/column — or rename to row/col.
cin Return ValueAvoid using uninitialized rows when the user types letters instead of a number.
Only call cout << "\n" after the inner loop finishes the row.
for (j = rows; j >= i; j--) with cout << i makes repeat count grow as the digit shrinks.
Trace rows = 3 on paper before coding larger demos.
Pro Tip: if the output is a vertical list of single digits per line, you almost certainly put cout << "\n" inside the inner loop.
Mistakes that commonly break descending repeating number patterns.
Each repeated digit lands on its own line — you get a column, not a triangle.
→ Use cout << i for repeats; cout << "\n" only after the inner loop.
j <= rows prints a rectangle; wrong outer bounds flatten or invert the shape.
→ For this shape, keep j <= i.
Omitting cout << "\n" glues every repeat onto one endless line.
→ Always end the row after the inner loop.
Letters or empty input leave rows unset if you ignore cin errors.
→ Check cin.fail() after cin >> rows and re-prompt on failure.
Switching to i = 0 without adjusting the inner bound prints an empty first row or wrong counts.
→ If 0-based, print i with wrong inner bound (e.g. j <= i + 1).
Check these inputs before calling the solution done.
Output is just one copy of rows on one line.
Outer loop never runs — print nothing or show a message.
rows < 0Treat as invalid; re-prompt instead of silent empty output.
Output grows as n²/2 characters — fine for labs, noisy for huge n.
Unchecked cin leaves rows unset — check cin.fail().
Check inner bound: j >= i gives rows - i + 1 repeats.
Try these variations to lock in the pattern.
for (i = rows; i >= 1; i--) as outer loopcin until rows >= 1cout << i << " " between repeated digitsn(n+1)/2 — hence O(n²) time.cout << i stays on the line; cout << "\n" advances — use both deliberately.rows > 0 for interactive programs; rows = 1 should print one copy of the top digit.Quick Takeaway: outer loop picks the row, inner loop repeats digit i, then break the line — that is the whole pattern.
| Program | Time | Extra space |
|---|---|---|
| Nested loops (Examples 1–2) | O(rows²) | O(1) |
string(rows - i + 1, char('0' + i)) in a counted loop (Example 3) | O(rows²) | O(rows) per row string (temporary) |
The descending repeating number triangle pattern is a small nested-loop exercise with lasting payoff: row/column thinking, cout vs row newline, and O(n²) intuition. Master the classic two-loop version, then optionally shorten rows with string(rows - i + 1, char('0' + i)) in a counted loop.
Practice the three examples above, then continue to Program 11 for the inverted repeating triangle.
Row i repeats digit i — keep cout << i for each copy and cout << "\n" for the break, and validate row counts when reading input.
cout << i for repeats and cout << "\n" after each rowrows ≥ 1 for interactive programscin.fail() before using rowscout << "\n" inside the inner repeat loopj <= i when you meant Program 9 insteadrows = 1 edge casePrint the triangle the beginner-friendly way.
Row i repeats digit i
DefinitionPicks the digit each row
CodeRepeats digit with cout << i
CodeEnds each row
I/OO(n²) time
AnalysisRow digit i repeats rows - i + 1 times. The outer loop counts down from rows, so the first row shows one copy of the top digit and the last row repeats 1 for rows times — still O(n²) total prints.
Same digits, but the widest row is first — 55555, 4444, 333, 22, 1.
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