Number Puzzle Strategy Guide - Master Sliding Tile Techniques & Algorithms

Introduction

Number Puzzle is a time-attack sliding tile game featuring six progressive stages with grid sizes from 3×3 to 5×6. Success requires mastering efficient solving algorithms, optimal move sequencing, and strategic time management. This guide teaches proven techniques used by expert puzzle solvers to minimize moves and maximize scores.

Scoring System Breakdown

Time Bonus Calculation

Each stage has a time limit. Leftover seconds multiply by a per-second bonus value that increases with difficulty:

• Stage 1 (3×3): 45s limit, +10 pts/second
• Stage 2 (3×4): 60s limit, +15 pts/second
• Stage 3 (4×4): 75s limit, +20 pts/second
• Stage 4 (4×5): 90s limit, +30 pts/second
• Stage 5 (5×5): 120s limit, +40 pts/second
• Stage 6 (5×6): 150s limit, +50 pts/second

Combo Multipliers

Completing stages without exceeding move thresholds builds your combo multiplier:

• Under optimal moves: +0.5× multiplier
• Perfect solve (minimum moves): +1.0× multiplier
• Max multiplier: 5.0×
• Timeout penalty: Reset to 1.0×

Optimal move counts: 3×3=15, 3×4=25, 4×4=40, 4×5=60, 5×5=85, 5×6=120 moves

Core Solving Algorithms

1. Row-by-Row Method (Beginner Friendly)

Best for: Stages 1-3 (3×3 to 4×4 grids)

Solve the puzzle systematically from top to bottom, left to right. Once you correctly place the top row, never move those tiles again.

Position tile #1 in top-left corner
Bring tile #2 to position (row 1, col 2)
Continue filling row 1 from left to right
Lock row 1, move to row 2 and repeat
For last 2 rows/columns, use rotational patterns

Average moves: 120-150% of optimal (acceptable for learning)

2. Edge-First Strategy (Intermediate)

Best for: Stages 3-5 (4×4 to 5×5 grids)

Solve perimeter tiles first, then work inward. This creates a "frame" that constrains the problem space.

Solve entire top row (left to right)
Solve entire bottom row (left to right)
Solve left column (top to bottom, excluding corners)
Solve right column (top to bottom, excluding corners)
Solve remaining center using row-by-row

Average moves: 105-115% of optimal (recommended for consistent scores)

3. Pattern Recognition Method (Advanced)

Best for: All stages, especially 5×6

Recognize common misplacement patterns and execute memorized solution sequences. Requires extensive practice but achieves near-optimal move counts.

Common Patterns:

• Two-tile swap: When two tiles are swapped, use 3-move rotation pattern
• Clockwise cycle: Three tiles rotated clockwise need 5-move counter-rotation
• Corner lock: Tile in wrong corner but correct quadrant: 7-move pattern
• Linear chain: Multiple tiles offset by 1 position: sliding cascade technique

Average moves: 95-100% of optimal (expert level)

4. Heuristic Solver (Expert)

Best for: Speedrunning and leaderboard competition

Mentally calculate Manhattan distance (sum of tile displacement distances) and choose moves that reduce total distance most efficiently. Requires quick mental math.

Formula: For each tile, distance = |current_row - target_row| + |current_col - target_col|

Always choose the move that reduces total Manhattan distance the most, while avoiding moves that create hard-to-solve patterns.

Stage-Specific Strategies

Stage 1: 3×3 Grid (8 tiles)

EASY

Optimal: ~15 moves | Time limit: 45s

Strategy: Use row-by-row. Solve row 1 (tiles 1-3), then position tiles 4-5 in row 2. The last 3 tiles (6-8) form a simple rotation that can be solved in 3-6 moves. Aim for 20-25 second completion to bank 20-25 seconds × 10 pts = 200-250 bonus points.

Stage 2: 3×4 Grid (11 tiles)

MODERATE

Optimal: ~25 moves | Time limit: 60s

Strategy: Edge-first works well. Solve all 4 corners first (tiles 1, 3, 9, 11), then fill edges. The 3-tile center can be solved with a simple clockwise/counter-clockwise pattern. Target 35-40 second completion for maximum bonus.

Stage 3: 4×4 Grid (15 tiles)

HARD

Optimal: ~40 moves | Time limit: 75s

Strategy: This is the classic 15-puzzle. Mandatory pattern recognition stage. Solve rows 1-2 completely (tiles 1-8), then solve columns 1-2 of rows 3-4 (tiles 9,13 and 10,14). The final 2×2 square has only 2 possible states—memorize both solutions (6 moves each).

Stage 4: 4×5 Grid (19 tiles)

VERY HARD

Optimal: ~60 moves | Time limit: 90s

Strategy: Edge-first is mandatory. Solve top row entirely (1-5), bottom row entirely (15-19), then left/right columns. The remaining 3×3 center solves like Stage 1. Do NOT attempt row-by-row from scratch—you'll exceed 100 moves and timeout.

Stage 5: 5×5 Grid (24 tiles)

EXPERT

Optimal: ~85 moves | Time limit: 120s

Strategy: Combination approach. Solve outer ring using edge-first (16 tiles), leaving inner 3×3 grid. Requires quick decision-making and strong pattern recognition. Most players timeout here—practice this stage specifically. Use Shuffle button if you spot an extremely difficult configuration.

Stage 6: 5×6 Grid (29 tiles)

MASTER

Optimal: ~120 moves | Time limit: 150s

Strategy: The final boss. Heuristic solver required for competitive times. Solve outer perimeter (18 tiles), then 3×4 interior using edge-first. Expect 150-180 moves on first attempts. Only top 10% of players complete this stage. Banking even 10 seconds = 500 bonus points, so every second counts.

Advanced Techniques

Look-Ahead Planning

Before moving any tile, mentally simulate the next 2-3 moves. This prevents dead-ends where you must undo progress.

Example: Moving tile X into position blocks access to tile Y. Instead, position Y first, then X.

Shuffle Strategic Use

Shuffle button randomizes tile positions without penalty. Use it when you spot configurations with high Manhattan distance (tiles far from targets).

Rule: If 5+ tiles are 3+ positions away from target, shuffle immediately.

Keyboard vs Touch

Arrow keys (desktop) are faster than tapping for rapid move sequences. Touch is better for visualizing multi-step patterns.

Hybrid: Use touch to plan, keyboard to execute. Reduces input errors by 30%.

Time Banking

Solve stages 1-3 as fast as possible to accumulate time for harder stages. Every second saved early = bonus points later.

Target: Finish Stage 3 with 75+ total banked seconds for stages 4-6.

Common Mistakes

❌

Moving Already-Correct Tiles

Once a tile is in its final position (especially in outer rows/columns), never move it again. Lock it mentally.

❌

Random Move Spam

Clicking frantically without a plan wastes moves and time. Every move should have purpose.

❌

Ignoring Move Count

Time bonus only matters if you complete the stage. Exceeding 200 moves usually means timeout.