A left-shifted odd number triangle prints consecutive odd numbers on each row while the starting odd value increases by 2 — so each row is shorter and shifts left.
Remember
Rule: for i = 1..max step 2, print j = i..max step 2
13579
3579
579
79
9 ← max = 9 (or 10 with odd-only loops)
In C# you solve it with nested loops that both step by 2: for (i = 1; i <= max; i += 2) and for (j = i; j <= max; j += 2), then WriteLine() ends the row. Start at 2 for an even-number mirror.
Approach
How to Solve It
Master the odd-only += 2 loops first, then optionally mirror with even starts.
Method
Idea
Best for
Odd += 2
Outer picks start odd; inner prints odds up to max
Learning step size, this pattern
Even mirror
Same structure starting at 2
Contrast / even-only variant
Pseudocode
Pseudocode
for i from 1 to max step 2:
for j from i to max step 2:
print j (no newline)
print newline
Cheat sheet
Goal
Pattern
Pick row start (odd)
for (i = 1; i <= max; i += 2)
Print odds to max
for (j = i; j <= max; j += 2) Console.Write(j);
End the row
Console.WriteLine();
Force odd max
if (max % 2 == 0) max -= 1;
Even mirror
for (i = 2; i <= max; i += 2) with the same inner shape
Write vs WriteLine
API
Effect
Use for
Console.Write
Stays on the same line
Each odd number j
Console.WriteLine
Ends the current line
After the inner loop
Try it
Live Preview
Change the maximum and the odd triangle updates instantly. Even values are adjusted down to the nearest odd number.
Whole numbers from 1 to 15. Even input becomes the next lower odd max (e.g. 10 → 9).
Live resultmax 9 · 15 numbers
13579
3579
579
79
9
Trace
Worked Walkthrough — max = 9
Trace each outer-loop value of i and the odd j values printed on that row.
i
Inner j
Printed row
Count
1
1, 3, 5, 7, 9
13579
5
3
3, 5, 7, 9
3579
4
5
5, 7, 9
579
3
7
7, 9
79
2
9
9
9
1
Total prints are 5+4+3+2+1 = 15 — triangular in the count of odd values up to max.
Code
C# Programs
Three complete programs: fixed max, input with odd forcing, and an even-number mirror. Use View Output for sample results.
Example 1 — Fixed max = 10
Both loops step by 2 from odd starts, so only odds print (up through 9).
C#
using System;
namespace MyApp
{
class Program
{
static void Main(string[] args)
{
int i, j;
for (i = 1; i <= 10; i += 2)
{
for (j = i; j <= 10; j += 2)
{
Console.Write(j);
}
Console.WriteLine();
}
}
}
}
Output
13579
3579
579
79
9
How It Works
1. Odd starts.for (i = 1; i <= 10; i += 2) yields 1, 3, 5, 7, 9 — the first number on each row.
2. Odds to max. When i = 1, the inner loop prints 13579; when i = 9, just 9.
3. Newline.WriteLine() after the inner loop starts the next shorter left-shifted row.
Example 2 — User Input
Read the maximum at runtime; force it odd if the user enters an even number.
C#
using System;
namespace MyApp
{
class Program
{
static void Main(string[] args)
{
int max;
Console.Write("Enter the maximum value: ");
if (!int.TryParse(Console.ReadLine(), out max) || max < 1)
{
Console.WriteLine("Please enter a positive whole number.");
return;
}
if (max % 2 == 0) max -= 1;
for (int i = 1; i <= max; i += 2)
{
for (int j = i; j <= max; j += 2)
{
Console.Write(j);
}
Console.WriteLine();
}
}
}
}
Output (when user enters 8)
1357
357
57
7
How It Works
1. Validate and force odd.TryParse rejects bad input; if (max % 2 == 0) max -= 1 turns 8 into 7.
2. Same nested loops. With max = 7, rows end at 7 instead of 9.
Example 3 — Even Number Mirror
Same left-shift structure, but both loops start at 2 and visit only even values.
C#
using System;
namespace MyApp
{
class Program
{
static void Main(string[] args)
{
int max = 10;
int i, j;
for (i = 2; i <= max; i += 2)
{
for (j = i; j <= max; j += 2)
{
Console.Write(j);
}
Console.WriteLine();
}
}
}
}
Output
246810
46810
6810
810
10
How It Works
1. Even starts.i = 2 and j += 2 visit 2, 4, 6, 8, 10 only.
2. Same left shift. Each row starts later, so the triangle shortens — compare with Example 1 to see how the start value changes the sequence.
Edge Cases & Pitfalls
Check these before calling the solution done.
wrong step
j++ instead of j += 2
That includes even numbers. Keep stepping by 2 for odd-only rows.
even max
Even maximum without adjustment
Odd-only loops still skip 10, but forcing max -= 1 makes the bound explicit when reading input.
WriteLine early
WriteLine(j) inside the inner loop
That puts each number on its own line. Use Write(j); call WriteLine() only after the row finishes.
max = 1
Single odd
Output is just 1 — a good sanity check.
max ≤ 0
Empty output
The outer loop never runs. Validate and prompt again for clearer UX.
multi-digit
Write(10) concatenates
The even mirror prints 246810 with no separators — fine for labs; use Write(j + " ") if you want spaced columns.
Analysis
Time and Space Complexity
Program
Time
Extra space
Odd loops (Examples 1–2)
O(n²)
O(1)
Even mirror (Example 3)
O(n²)
O(1)
About k = (n+1)/2 odd values produce k(k+1)/2 prints — still quadratic in the maximum n.
Remember
Key Takeaways
Rule: for odd i from 1 to max, print odd j from i to max.
Step by 2:+= 2 on both loops is what keeps the output odd-only.
Write vs WriteLine: numbers stay on the line; WriteLine advances after each row.
Next step: Program 18 alternates odd and even rows.
One line: for each odd start from 1 to max, print odds from i to max with Write, then WriteLine.
Frequently Asked Questions
Both loops increment by 2 (i += 2 and j += 2), so they visit only odd values: 1, 3, 5, 7, 9.
Each next row starts from a larger odd number (i increases by 2), so fewer digits print on that row.
On the last iteration, i = 9, so the inner loop prints only 9 once.
Console.Write stays on the same line. Console.WriteLine ends the current line. Digits use Write(j); the row break uses WriteLine after the inner loop.
Not with += 2 starting from odd numbers — that visits only odd values. To include 10, use j++ or handle even values separately.
Subtract 1 (max -= 1) so the last printed odd matches the intended width, as shown in Example 2.
O(n²) for maximum value n. Only about half the numbers are visited due to step size 2, but nested loops still dominate.
Prefer int.TryParse(Console.ReadLine(), out max) so bad input does not throw FormatException.
The outer loop never runs, so nothing is printed. Validate and prompt again if you want a clear user message.
🤔
Did you know?
Both loops step by 2 with i += 2 and j += 2, so only odd numbers print. Each row starts at a larger odd value, so the triangle shifts left — still O(n²) for maximum n.
