Magic Square

This program generates a 3×3 magic square starting from a user-supplied beginning number and a common difference between successive values. The nine values are stored in a one-dimensional array of nine elements, with each element computed as an arithmetic sequence using the starting value and step size. The square is displayed on screen with rows printed using AT coordinates, and the sum of any row, column, or diagonal is calculated and shown beneath the grid. A second, largely duplicated block of code starting at line 1200 handles printing the same square to a printer via LPRINT with TAB-aligned columns, looping continuously to allow repeated printouts.

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Program Analysis

Program Structure

The program is divided into two largely independent blocks separated by a STOP at line 1190. The first block (lines 190–1190) handles screen display, while the second block (lines 1200–1450) handles printer output. Line 9990 contains the SAVE command with an auto-start directive.

Line Range	Purpose
190–320	CLS and input collection with basic validation
400–410	Array initialization and arithmetic sequence computation
420–450	Screen display of the 3×3 grid and magic sum
1190	STOP — ends screen-only execution path
1200–1450	Duplicate input/compute block with LPRINT output, loops indefinitely
9990	SAVE with auto-start

Magic Square Construction

The nine values are stored in array a(9) as an arithmetic sequence: a(1) is the base value, and each subsequent element increments by step z. The mapping from array indices to grid positions encodes the classic Lo Shu magic square arrangement:

• Top row: a(8), a(1), a(6)
• Middle row: a(3), a(5), a(7)
• Bottom row: a(4), a(9), a(2)

This arrangement guarantees that all rows, columns, and diagonals sum to the same value, which is then displayed using the expression a(8)+a(1)+a(6) (the top row sum).

Input Validation

Validation at lines 210 and 310 uses string comparison rather than numeric comparison. The check a$<"1" OR a$>"999" is lexicographic, not numeric, meaning values like “500” would pass but so would certain edge-case strings. The lower bound check for the difference (b$<"1") only rejects strings that sort before “1” lexicographically, which would allow non-numeric strings starting with digits 1–9 or letters.

Notable Techniques

• The counter variable y is initialized to 1 before the FOR loop and incremented inside it, so a(x) = a(1) + y*z correctly assigns multiples 1 through 8 of the step to elements 2 through 9.
• Screen layout uses AT row/column coordinates to position numbers in a visually aligned 3×3 grid.
• The printer block uses LPRINT with TAB stops (columns 5, 10, 20) to align columns and append the row sum inline on the middle row.
• The printer block at line 1450 uses GO TO 1200 to loop indefinitely, allowing the user to print multiple copies with different parameters without restarting.

Bugs and Anomalies

The screen and printer blocks are almost entirely duplicated code rather than shared via subroutines. The screen block (lines 190–1190) is never called from the printer loop, meaning the two modes of operation are mutually exclusive and the program must be run from line 190 for screen output or from line 1200 for printer output. There is no menu to select between the two modes.

The input validation at line 1210 incorrectly branches to GO TO 200 (inside the screen block) instead of GO TO 1200, which would disrupt the printer loop’s flow by jumping into the screen-display path.