path-to-one: Cursed Labyrinth

path-to-one is a math roguelike game based on the Collatz conjecture (3n+1 problem). Choose a "cursed number" and navigate a dark labyrinth where every room is a mathematical challenge. Odd rooms are dangerous — the curse swells with 3n+1, dealing damage. Even rooms offer brief safety — divide by 2 and press on. Your goal: reach 1 to break the curse. STRATEGIC COMBAT Every odd room presents a choice: fight head-on (3n+1), take a detour (n+1) for a card, use spell cards, or flee. Each decision affects your curse chain — consecutive odd rooms amplify damage up to 2x. In even rooms, press on, rush ahead, or take a risky bet. SPELL CARDS Start with 6 single-use spell cards from 7 types. Halve your number, subtract from it, shield against damage, heal HP, peek ahead, accelerate through rooms, or purify to even. Duplicate cards upgrade to powerful enhanced versions. 7 ENEMY TIERS From Cursed Slimes to the God of Ruin, each enemy tier brings unique abilities: Dark Fog negates foresight, Piercing cuts through shields, Despair triples erosion damage. 6 BUILDS AND 4 DIFFICULTY TIERS Choose from Guardian, Accelerator, Sorcerer, Seer, Contractor, or the premium Overlord — each with unique starting hands and playstyles. Challenge Normal, Abyss, End, or Void difficulty for greater rewards. WEEKLY CHALLENGE (OPTIONAL) Every week, players worldwide take on the same cursed number under the same conditions (Guardian build, Normal difficulty) and compete with their best score of the week on "This Week's Ranking". Joining is consent-based: nothing is sent until you choose a nickname and tap "Agree and register". Link your Apple ID or Google account (optional) to carry your record and nickname over to a new device or a reinstall. You can delete your account and ranking records from within the app at any time (Weekly Challenge > "Account" > "Delete account"). WEEKLY CHAMPION REWARD The week's #1 (on a tie, whoever reached that score first) chooses the cursed number for the week after next: any number from 100 to 9999 that takes at least 70 steps to reach 1. The choice can be changed until Sunday 23:55 (JST), and that week's screen shows the chooser's nickname. DAILY CHALLENGE A unique seeded number every day, one attempt per day. Clear it for 1.5x score and 2x Curse Marks. DAILY REMINDER On days you haven't played the Daily Challenge yet, a notification reminds you around 18:00. Permission is requested after your first finished run, and you can turn it off in your device settings at any time. The reminder is scheduled on your device; nothing is sent externally. COMBO SYSTEM Clear consecutive rooms without taking damage to build a streak. Up to 100 bonus points added to your final score. DEEP PROGRESSION - 19 achievements to unlock - Grimoire tracks all enemies, cards, and events - Curse Marks currency to unlock builds and difficulties - Score ranking system (D through S rank) - Adventure records to track your history - 4 derived events unlock through repeated play RANDOM EVENTS Healing springs, curse traps, treasure chests, dark merchants — and their enhanced variants unlock after repeated encounters. 16 LANGUAGES English, Japanese, Chinese (Simplified), Chinese (Traditional), Spanish, Portuguese (Brazil), Korean, German, French, Hindi, Indonesian, Russian, Italian, Turkish, Thai, and Vietnamese. IN-APP PURCHASES (ONE-TIME) The game is free to play. Three optional items are available, each a one-time purchase that stays unlocked. Use "Restore Purchases" on the title screen after a reinstall. - Remove Ads: hides all ads - Unlock Number Input: choose any starting number from 2 to 9999 - Overlord Build: unlocks the Overlord build, strong in offense and defense ABOUT ADS A banner is shown at the bottom of the screen and a full-screen ad after you tap a button on the result screen. You can change how ads are shown at any time from "Ad settings" on the title screen. Can mathematics save you from the curse?