Zero Sum

About the Game

Zero Sum is a pencil-on-paper twin-stick puzzle-roguelite. Your enemies are live integers and your weapons are operators. No health bars. No bullet sponges. Just raw arithmetic violence.

A "48" is charging at you. You fire ÷2. Now it's "24". Three more divisions: "12," "6," "3." Now switch to minus. Bang. Bang. Bang. Zero. Gone. Next.

Build lethal operator synergies across 6 distinct arenas and 3 combat rule sets. Face 9 multi-stage bosses built around weaponized mathematical concepts. Customize your loadout across 7 operators and 22 unlockable firing modes. From rapid-fire setups and execute shots to chain-division, square-root walls, modulo mines, and screen-warping Sigma vortexes.

Enemies aren't just walking health bars. Every number dictates how you have to fight it. A prime number shrugs off clean division until you nudge its value with + or −. A factorial splits and grows exponentially if you ignore it. Negatives invert your setup. You can't just hold down the trigger and backpedal. Don't just shoot, solve!

Forget guns. You carry operators. Minus and Plus are your precision setup tools, manipulate awkward primes into clean multiples with Optimizer or vaporize stragglers with Execute. Division cleaves high-value targets in half. Root shatters massive squares into rubble. Modulo nukes even the biggest numbers in a single hit if played right. Multiplication drops slowing traps and freeze lines that lets you control the playing field. And then there's Sigma, vacuum a massive swarm of small numbers into one giant, clean-divisible, easy to handle target.

Seven operators. Twenty-two firing modes to unlock. Every shot is a tactical decision. Every clean kill and multi-operator setup rewards bonus points. Integer split, perfect root, modulo chain. The game knows when you're showing off and pays you for it.

Every kill can be a clean kill. Divide a number without a remainder. Root a perfect square down. Land a modulo that leaves exact zero. Fire a sloppy shot, and you'll create more enemies and break your streak.

Chain clean kills across different operators to build massive Clean Combo Multipliers. Perfect wave? No messy remainders? Huge bonus payouts. The flashier the setup, the faster your build snowballs.

Sloppy kills keep you alive, but clean math makes you rich. In Zero Sum, showing off pays off.

Run one, you're rationing division ammo. Do you minus this 72 down shot by shot, or spend division ammo for the clean combo? Do you root the cluster of 16s for instant clears, or hold it for the tanky 256 barreling toward you?

Run twenty, your chain-divides ricochet through swarms, your root shotgun pulps clusters in a single blast, and your Sigma vortex eats half the screen. Unlock permanent alterations on a 100+ node Skill Tree between runs, and draft high-risk, high-reward wave modifiers within them. Every death makes the next run meaner.

Standard Mode is the core roguelite loop across multiple paper arenas. From classic chokepoints and shielded conveyor belts to corridor holdouts and wide open boss arena rushes. Chain smart math, gamble on shop curses, aim for Perfect Waves, and harvest boss trophies.

Verdict Mode is a high-stakes precision gauntlet. Operators like ÷, √, and % either solve a number cleanly or punish you. Know your math to survive this mode.

Target Mode flips the script. Instead of reducing enemies to zero, transform each number into a specific target value using +, ×, and Σ within a strict operation limit.

Zero Sum includes a full in-game Problem Set & Challenge Editor. Design custom tactical puzzles with your own wave sequences, number patterns, fixed operator loadouts, traps, and resolution rules. Built-in validation catches unsolvable configurations before you export.

Every problem set compresses into a shareable code. Copy it, paste it, drop it in Discord, or dare your friends. Anyone can import your code, get graded on a Report Card and send their result code back to prove they beat your score.

Set your own grade thresholds, customize the teacher's name, and write your own snarky per-grade verdicts.

Nine multi-phase bosses, each built around a mathematical concept that wants you dead (a small selection):

The Euler Owl

• a wise predator firing Taylor-series projectiles that duplicate in flight. Cut off the expansion before the screen overflows.

The Factorial Factory

• a heavy fortress launching factorial shells. 9! detonates into 9 × 8 × 7 × 6 × …, trying to recombine into their product. Collapse the pieces to zero before they merge.

The Pi Boss

• a spinning pie armored by the digits of π. Strip away each slice in sequence to crack its shell into weak points.

The Yin-Yang Harmony

• two orbiting halves, one positive, one negative. Over-damage one side and the other goes berserk. Balance the harmony meter or get swarmed.

The Prime Sieve Spider

• an eight-legged nightmare whose web is a live Sieve of Eratosthenes. Destroy the composite numbers while avoiding prime traps, shoot a prime and it breaks free to hunt you down.

Zero Sum looks like your notebook came alive and chose violence. Enemies are the doodles you drew in class, except these doodles want revenge.

• 7 operator weapons with 22 firing modes: transform how every operator behaves. From bouncing modulo chains and root walls to contextual plus-optimizers

• 100+ skill tree nodes & shop modifiers: unlock permanent weapon alterations between runs and stack high-risk wave curses within them

• 9 bespoke boss fights built around weaponized math: Taylor series, prime sieves, factorials, matrices, nested shells, vectors, harmonic balance, pi, sigma

• 6 arenas & 3 combat rule sets: Standard roguelite runs, endless Verdict mode survival with mid-run operator drafting, factor-hunting Book Pages, and Target puzzle combat

• Full Challenge Editor & Share Codes: build custom problem sets with custom waves, loadouts, and grading rules, then share compact codes and verify Report Cards

• Global Steam Leaderboards & Achievements: compete for the highest scores on each map and difficulty

• 3 difficulty tiers that escalate wave pressure and unlock lethal new boss phases on Hard

• Crisp twin-stick controls with full mouse + keyboard and controller support

• A skill ceiling made of speed, synergy, and mental calculation.