A normal 3×3 magic square uses digits 1–9 exactly once; each row, column, and diagonal sums to 15. You can construct one by the classic Siamese (de la Loubère) walk—or solve a partially blank grid by treating lines as equations and enforcing uniqueness. ProPuz usually presents a masked version of a fixed solution; your goal is to recover that stored pattern. The steps below work for reasoning; always align with the app’s check feature for the authoritative answer.
Step 1: Memorize M = 15
Compute from the formula n(n²+1)/2 with n = 3, or add 1+…+9 and divide by three rows. Fifteen is your North Star.
Step 2: List missing numbers
Track which of 1…9 remain unused. Duplicates violate normality and will eventually break a line sum.
Step 3: Attack nearly complete lines
Any row, column, or diagonal with two cells filled yields the third by subtraction from 15.
Step 4: Use both diagonals early
Diagonals cross the center; in the classic 3×3 normal square the center is 5—useful prior when learning, but on scrambled puzzles derive it from constraints instead of assuming.
Step 5: Construction preview (optional)
Learning the Siamese placement algorithm builds intuition for why certain cells correlate; see create your own.
Step 6: Verify before celebrating
Re-sum every line; one diagonal slip undoes the “magic” label. Use ProPuz check to catch slips faster.
Worked mindset: two filled cells on a row
Suppose the top row shows 8 and 1. The missing corner must be 15 − 8 − 1 = 6 if that placement respects unused digits elsewhere. If 6 already lives in the grid, your clues imply a contradiction—revisit earlier assumptions rather than forcing the arithmetic.
This “complete the triple” micro-step appears dozens of times per solve. Experienced solvers batch them: scan all rows/columns/diagonals with exactly two givens or player entries, fill everything forced in one sweep, then repeat until the puzzle advances.
Intersections beat isolated cells
A blank at the crossing of a nearly complete row and column is doubly constrained. Write candidate sets mentally: which digits can still sit here without duplicating and without breaking either line’s future? On 3×3, candidate sets shrink to singletons quickly—this is shallow constraint propagation, not guesswork.
When to reveal on ProPuz
Pedagogically, a single reveal after two stuck minutes can unblock pattern recognition. Spamming reveals hides the arithmetic lesson—alternate reveals with manual re-verification so your eye still tracks diagonals.
From manual solve to construction literacy
Once solving feels reliable, learn construction to appreciate why certain triples cohabit lines. The bridge article create your own magic square walks the Siamese path that ProPuz uses server-side for odd orders.