A 10×10 Shikaku grid has 100 cells — the largest standard size and the true test of rectangle partition mastery. Expect 30-60 minute solve times and deeply rewarding "aha" moments.
100 cells — a perfect square (10²), four times the area of 5×5
15-25 rectangles — complex partitioning with many interdependencies
Numbers up to 100 — introduces numbers with 6+ factor pairs
30-60 minute solve time — a proper puzzle marathon
10×10-Specific Strategies
The "100 Check"
All numbers must sum to 100. With 15-25 numbers, use grouping: pair numbers that sum to 10, 20, or 25 for quick mental math.
Zone Partitioning
Divide the 10×10 grid mentally into four 5×5 quadrants. Solve each quadrant semi-independently, then reconcile the borders. This reduces cognitive load from "100 cells" to "four 25-cell puzzles."
High-Number Anchors
Numbers above 50 are extremely constrained:
Number
Fit in 10×10?
Shape
60
6×10, 10×6
Covers 60% of grid
72
8×9, 9×8
Covers 72% of grid
80
8×10, 10×8
Covers 80% of grid
90
9×10, 10×9
Covers 90% of grid
96
—
Doesn't fit! (needs 12×8 or wider)
The "Factor Explosion" Problem
Mid-range numbers like 36, 48, 60 have many factor pairs. A "60" can be 2×30, 3×20, 4×15, 5×12, 6×10, 10×6, 12×5, 15×4, 20×3, 30×2 — but only 6×10 and 10×6 fit in a 10×10 grid. Always filter by grid dimensions first.
Essential Factor Reference
Number
Factor Pairs (fit in 10×10)
Difficulty
12
2×6, 3×4, 4×3, 6×2
Easy — 4 options
24
3×8, 4×6, 6×4, 8×3
Medium — 4 options
36
4×9, 6×6, 9×4
Medium — 3 options
48
6×8, 8×6
Hard — 2 options
60
6×10, 10×6
Hard — 2 options
72
8×9, 9×8
Very hard — 2 options
Master Technique: Constraint Propagation
1List all possibilities. For each number, write down every rectangle that fits in the grid AND doesn't overlap with confirmed placements.
2Find forced placements. If a number has only one valid rectangle, place it immediately. This is the "naked single" of Shikaku.
3Propagate constraints. Each placement eliminates possibilities for neighboring numbers. Re-check affected numbers after every placement.
4Use "what's left" reasoning. If a region has 8 uncovered cells and the only unplaced number in range is "8", it must fill the entire region — regardless of shape options.
💡 Pro Tip: For 10×10 puzzles, use paper or a notes app to track factor pairs. Mental math errors compound fast at this size — a single wrong placement can cascade into an unsolvable state 20 moves later.