4096 Game Challenge
Play the addictive 4096 logic puzzle. Merge tiles to reach the 4096 tile. Features auto-save, high scores, and fluid animations. Train your brain now.
HOW TO PLAY: Use Arrow Keys or swipe to move tiles. Tiles with the same number merge into one!
About
The 4096 Challenge is a mathematical sliding block puzzle that exploits the properties of exponential growth. The objective is to slide numbered tiles on a grid to combine them and create a tile with the number 4096. The game logic rests on the power of two: 2n. While it appears simple, the rapid escalation of values requires forward-thinking strategy to avoid gridlock.
Unlike simple arithmetic games, this tool simulates a confined system where entropy (disorder) increases with every move. Each swipe introduces a new random variable (a 2 or 4 tile), reducing the available free space S. The risk of failure occurs when S → ∅ (empty set) and no adjacent values satisfy xi = xj.
Formulas
The scoring function Score accumulates the sum of all merged tiles. When two tiles of value v merge, the score increases by:
Where k is the number of merges in a single turn. The minimum theoretical score to reach 4096 involves summing the partial products of the chain:
Reference Data
| Power (n) | Value (2n) | Tile Color | Probability |
|---|---|---|---|
| 1 | 2 | Beige | 90% Spawn |
| 2 | 4 | Cream | 10% Spawn |
| 3 | 8 | Light Orange | Merge Only |
| 4 | 16 | Orange | Merge Only |
| 5 | 32 | Burnt Orange | Merge Only |
| 6 | 64 | Red-Orange | Merge Only |
| 7 | 128 | Yellow-Gold | Merge Only |
| 8 | 256 | Goldenrod | Merge Only |
| 9 | 512 | Gold | Merge Only |
| 10 | 1024 | Amber | Merge Only |
| 11 | 2048 | Dark Gold | Major Milestone |
| 12 | 4096 | Black/Gold | TARGET |