🧩 Puzzles & Constraints
Grid puzzles, digit codes, and balance problems
🧩 Constraint puzzles
These are the "fill in the grid" problems — magic squares, digit puzzles, and balance puzzles. The strategy is always the same: start where you have the most information.
Find the cell with the fewest possibilities. Fill it. Repeat.
🔤 Letter-digit puzzles
PAPAYA: P, A, Y are different digits. Y = P+P = A+A+A.
- Y = 2P and Y = 3A
- So 2P = 3A → P = 3A/2
- P must be a whole number, so A must be even
- Try A=2: P=3, Y=6. All different ✓
- P×A×P×A×Y×A = 3×2×3×2×6×2 = 432
⬜ Grid-filling rules
When a grid requires each row and column to have the same sum (or different values), work from what's given:
- Step 1: Calculate what the row/column sum must be
- Step 2: Use known cells to find unknowns (sum minus known = unknown)
- Step 3: Check every constraint is satisfied
Example: A 5×5 grid with 0s and 1s where every row, column, and diagonal sums to 3. If the grid is 5×5, each row has 3 ones and 2 zeros. One cell is given as 0 — from there, you can deduce many others.
⚖️ Balance puzzles
When blocks are stacked and balanced, same-shaded blocks weigh the same. Set up equations:
- Left side total weight = Right side total weight
- If you see 2 dotted + 1 cross = 1 dotted + 3 solid, then 1 dotted = 3 solid − 1 cross
- Substitute into other equations to find the ordering
🧠 Practice Quiz
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