Follows the alternating 1/0 pattern in Program 40; next is the hollow square border of 1s in Program 42.
Approach
How to Solve It
One odd-step outer loop with indent, then a continuous square counter — pads with " ", values with f"{m*m:4d}".
Method
Idea
Best for
Centered pyramid
Indent, then print m*m with :4d
Learning, interviews, exams
Levels input
Same logic with max_width = 2*levels - 1
Practice / demos
Pseudocode
Pseudocode
maxWidth = 2 * levels - 1
m = 1
for i from 1 to maxWidth step 2:
for j from i to maxWidth-1:
print two spaces
repeat i times:
print m*m (width 4), then m = m + 1
print newline
Cheat sheet
Goal
Pattern
Odd row widths
for i in range(1, max_width + 1, 2):
Center the row
for j in range(i, max_width): print(" ", end="")
Next square
print(f"{m * m:4d}", end=""); m += 1
End the row
print()
Printing Numbers vs Starting a New Line
API
Effect
Use for
print(" ", end="") / print(f"{m*m:4d}", end="")
Stays on the same line
Each indent or square
print()
Ends the current line
After both inner loops
Print indents and squares without a newline, then end the row once.
Try it
Live Preview
Change the level count and the square pyramid updates instantly — capped at 5 for readable demos.
Whole numbers from 1 to 5 (keeps width-4 columns readable). Tap a chip or type a value — the preview redraws as you go.
max_width = 5. Trace indents and the running square counter.
i
Indent / squares
Printed row
1
4 pads / 1
1
3
2 pads / 4 9 16
4 9 16
5
none / 25..81
25 36 49 64 81
Total squares for n levels = n². Counter m never resets between rows.
Code
Python Programs
Three complete programs: fixed 5 levels, input() levels, and a compact 3-level demo. Use View Output to reveal sample results.
Example 1 — Fixed levels = 5
Odd-step outer loop; indent, then print continuous m*m with width-4 formatting.
Python
max_width = 9
m = 1
for i in range(1, max_width + 1, 2):
for j in range(i, max_width):
print(" ", end="")
for k in range(1, i + 1):
print(f"{m * m:4d}", end="")
m += 1
print()
1. Odd widths.i takes 1, 3, 5, 7, 9 — that many squares print on each row.
2. Indent. Print " " while j runs from i to max_width - 1 so the tip stays centered.
3. Continuous m. Print m*m with f"{m*m:4d}", then increment m — never reset between rows.
Example 2 — User Input Levels
Read levels with input(), set max_width = 2 * levels - 1, then use the same pyramid logic.
Python
try:
levels = int(input("Enter levels: "))
except ValueError:
print("Please enter a positive whole number.")
raise SystemExit(1)
if levels < 1:
print("Please enter a positive whole number.")
raise SystemExit(1)
max_width = 2 * levels - 1
m = 1
for i in range(1, max_width + 1, 2):
for j in range(i, max_width):
print(" ", end="")
for k in range(1, i + 1):
print(f"{m * m:4d}", end="")
m += 1
print()
Output (when user enters 3)
Enter levels: 3
1
4 9 16
25 36 49 64 81
How It Works
1. Prompt and validate. Catch ValueError; require levels >= 1 before printing.
2. Same core. Three levels end at 81 with nine squares total.
3. Safer input tip. Cap demos for readable width-4 columns:
Safer input tip
if levels < 1 or levels > 5:
print("Enter a whole number from 1 to 5.")
raise SystemExit(1)
Example 3 — Compact levels = 3
Same structure with only three levels — easy to confirm odd widths and continuous m.
Python
levels = 3
max_width = 2 * levels - 1
m = 1
for i in range(1, max_width + 1, 2):
for j in range(i, max_width):
print(" ", end="")
for k in range(1, i + 1):
print(f"{m * m:4d}", end="")
m += 1
print()
Output
1
4 9 16
25 36 49 64 81
How It Works
1. Same rules. Odd i sets count; indent; print the next squares.
2. Quick check. The base row has five values ending at 81.
3. Scale up next. Once the small demo is clear, use Examples 1–2 for five levels or user input.
Edge Cases & Pitfalls
Check these before calling the solution done.
reset m
Reset m = 1 each row
That restarts squares every line. Keep m outside the outer loop.
step 1
Loop i by 1 instead of 2
You get even widths too and lose the classic pyramid shape. Keep range(..., 2).
no :4d
Print m*m without width
Columns drift once values hit three digits. Prefer f"{m * m:4d}".
pad mismatch
Indent with one space
Pads should match half the number width — use " " (2 spaces) with :4d.
levels = 1
Single square
Output is just the formatted 1 — one level, one square.
input()
Catch ValueError
Bare int(input()) crashes on non-numeric text — wrap it in try/except ValueError.
Analysis
Time and Space Complexity
Program
Time
Extra space
Fixed / input (Examples 1–2)
O(n²)
O(1)
Compact levels = 3 (Example 3)
O(n²)
O(1)
Total printed squares are 1 + 3 + 5 + … + (2n−1) = n², so work is quadratic in the level count.
Remember
Key Takeaways
Rule: odd row widths via step 2; each cell prints the next m*m.
Center: indent with " " before printing the squares on each row.
end="" vs print(): indents and squares stay on the line; bare print() advances after each row.
Complexity:O(n²) time; O(1) extra space.
One line: for each odd width, indent then print the next perfect squares from a shared counter.
Frequently Asked Questions
A centered pyramid of perfect squares: for 5 levels you get 1 / 4 9 16 / 25..81 / … / 289..625 — consecutive m² values in odd-width rows.
The outer loop increases i by 2 each time (range(..., 2)), so i takes odd values — each becomes the count of squares printed on that row.
An indentation loop prints two spaces before each row. As i grows, fewer pads are printed, so wider rows shift left and stay centered.
m starts at 1 and increments after every printed square. Each value printed is m*m — the next perfect square in sequence.
Fixed-width columns keep the pyramid aligned as squares grow from 1 to 625. Without it, columns drift apart.
Program 40 alternates 1 and 0 with shrinking rows. Program 41 prints perfect squares in a centered pyramid with growing odd-width rows.
Use try/except ValueError around int(input()) and require levels >= 1 — see Example 2.
O(n²) for n levels — total prints are 1+3+5+…+(2n-1) = n².
🤔
Did you know?
Each printed value is m² from a running counter m. Row widths are odd (1, 3, 5, 7, 9) — total prints for n levels = n².
