How to Play FibDefense
Tower defense reimagined around mathematics. Every shot, every kill, every strategy is governed by the Fibonacci sequence.
The Exact-Kill Rule
A tower fires when a monster's remaining HP is greater than the tower's damage — meaning it can only contribute without overkilling. Chain your Fibonacci towers so their shots sum precisely to each enemy's HP, leaving nothing left over.
See It In Action
A tower fires when the monster's remaining HP is greater than the tower's damage — it won't fire if it would overkill. Your job is building the right sequence so HP reaches exactly zero.
✅ Good sequence — HP: 8
❌ Wrong tower — HP: 8
✅ Good sequence — HP: 13
The Eight Tower Tiers
Each tier deals exactly its Fibonacci number in damage. Higher tiers cost more to place but hit harder.
Zeckendorf's Theorem
Every positive integer can be written as a sum of non-consecutive Fibonacci numbers — and there is exactly one way to do it. This is called Zeckendorf's representation, and it's the mathematical engine behind FibDefense.
Because every enemy HP value has a unique Fibonacci decomposition, there's always a correct sequence of towers that can defeat it — you just have to find it.
Worked Examples
Waves & Progression
Each wave sends a new set of enemies down the path. HP values increase as you progress, demanding higher-tier towers and more complex Fibonacci combos.
Classic Mode
Endless Mode
Boss Encounters
At the end of certain waves, a Boss appears. Bosses have enormous HP values — between 500 and 2500 — requiring long chains of Fibonacci tower coverage across your entire path.
Boss HP is always a valid Fibonacci sum — there's always a solution, but finding it under pressure is the challenge.
Difficulty Levels
Choose your challenge. Easy is free — unlock premium to access the full gauntlet.
Strategy Tips
Plan your path layout before placing towers. Once a tower is down, rearranging costs resources.
Think of each enemy's HP as a Zeckendorf equation to solve. Write it out if you need to.
Higher-tier towers don't replace lower ones — you need both. A Tier-8 tower (34 dmg) can't handle a HP:3 enemy.
Bosses require full-path coverage. Make sure every Fibonacci tier is represented somewhere on the route.
On higher difficulties, enemy HP values arrive faster. Pre-plan your Fibonacci coverage for common HP values.
The sequence 1, 2, 3, 5, 8, 13, 21, 34 can sum to any integer up to 63. Knowing this ceiling helps you anticipate enemy HP caps per wave.
Ready to Test Your Math?
Download FibDefense and start with Easy mode — free forever.