πŸ”²Math Games

Number
Puzzle

// Fifteen Puzzle β€” Classic

Slide numbered tiles to arrange 1–15 on a 4Γ—4 grid. One empty cell β€” infinite paths. Find the shortest route.

4Γ—4 grid15 tilesNo time limit
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
// hover to interact

15-Puzzle

Slide tiles to arrange numbers 1-15 in order.

Mechanics

How the Puzzle Works

// the fundamental sliding mechanic

πŸ”²
Empty Cell

A single cell stays empty. Only tiles adjacent (up, down, left, right) to the empty cell can slide into it.

↔️
The Slide

Click a numbered tile adjacent to the empty space to slide it in. No lifting, rotating, or jumping over tiles allowed.

🎯
Goal State

Arrange all 15 tiles in order 1–15 reading left-to-right, top-to-bottom. Empty cell sits at the bottom-right corner.

Move Counter

Why Count Your Moves?

// every move has a cost

// CURRENT MOVES
0
7
2

Every tile slide increments the counter by 1. The optimal solution for an average 4Γ—4 puzzle takes around 52 moves. Expert players aim for under 80 moves.

~52
Theoretical optimal
< 80
Expert player
100–200
Beginner range
Strategy

The Row-by-Row Method

// foundational strategy for beginners

01
Phase 1
Top Row First

Place tiles 1–4 in the correct top row. Use rotations to slot them without disturbing each other.

02
Phase 2
Second Row

Place tiles 5–8 in the second row using the same row-by-row technique.

03
Phase 3
Left Column

Handle the left column (9 and 13) with a special L-shaped rotation move.

04
Phase 4
Final 2Γ—2

Solve the remaining 2Γ—3 or 2Γ—2 block using cyclic rotations until complete.

Difficulty

3Γ—3 vs 4Γ—4 vs 5Γ—5 β€” How Hard Is It?

// complexity scales exponentially

Size
Tiles
Avg moves
Level
3Γ—3
8
~20
Easy
4Γ—4
15
~52
StandardPLAYING
5Γ—5
24
~200+
Expert

// The 5Γ—5 puzzle has ~10^25 states β€” even powerful computers struggle to solve it optimally.

Pro Tips

Expert Advice

// cut moves, increase speed

01

Row by row

02

Corners last

03

Plan ahead