# Hamiltonian — Millennium Prize Problems

> Educational puzzle game based on finding Hamiltonian circuits in graphs. (iPhone/iPad app by 奕鑫 史.)

- Source: https://appshunter.io/ios/app/hamiltonian/id1309398796 (this page in markdown: same URL + `.md`)
- Developer: [奕鑫 史](https://appshunter.io/developer/1217732173)
- Category: Education, Entertainment
- Price: $0.99 with in-app purchases
- Rating: 4.00/5 from 8 App Store ratings · 21 written reviews indexed
- Age rating: 4+
- Requires: iOS 9.0 · 22 MB
- Languages: American English, Chinese (Simplified, China), Chinese (Traditional, Taiwan)
- Released: 2017-12-01
- Data updated: 2026-08-24
- Monetization: paid
- User reviews in markdown: https://appshunter.io/ios/app/hamiltonian/id1309398796/reviews.md

## What is Hamiltonian?

The design of Hamiltonian is inspired by Hamiltonian graph.

Each level is a Hamiltonian graph, and you need to find a Hamiltonian circuit to pass the level.
However, finding the Hamiltonian circuit is a P versus NP problem -  one of the Millennium Prize Problems.

The rule is very simple:
Find a walk in the graph that visits every vertex exactly once without repeating the edges and returns to the starting vertex.

Levels are easy to difficult in design. The front level is designed very simple, and the subsequent level will slowly increase the difficulty.
Each player will eventually be stuck on a level. You'll become smarter when you pass the stuck level.

Who will love it?
• Those who is clever
• Those who love challenges
• Those who want to be clever
• Those who want to know clever people

## Key features

- Hamiltonian circuit puzzles
- Progressive difficulty levels
- Problem-solving skill enhancement
- Graph theory challenges
- Brain-training gameplay

## Pricing and in-app purchases

Base price: $0.99.

**One-time purchases**

| Purchase | Price | Type |
| --- | --- | --- |
| 6 star coins | $0.99 | one-time |
| 15 star coins | $1.99 | one-time |
| 45 star coins | $3.99 | one-time |


## Recent user reviews (10 of 21)

All indexed reviews: https://appshunter.io/ios/app/hamiltonian/id1309398796/reviews.md

### 1/5 — 无法登录

*2023-01-20*

通过苹果账号方式无法登录

### 5/5 — 可以的

*2021-11-20*

智商居然是一点点提高的，哈哈

### 5/5 — 挺有意思的游戏

*2021-06-11*

没广告，至少我玩的时候没有……第一次接触这种玩法，一开始总想成一笔画有点不适应，后来就习惯了，并且发现其实有技巧……有几关也挺难的。但是这个排名统计感觉就不太准了，最后得了156就显示是第一，看到评论区160以上的大有人在，统计肯定是有问题的。希望这方面能完善

### 5/5 — 快乐的二刷

*2020-11-22*

在游戏作者的提醒/鼓励下，注册了微博账号来再挑战一次。
满足了自尊心，但其实最后好几道难题做过了，有作弊成分，题还是太少了，不过反正我挺高兴的就给五星了。
玩的人确实挺少的，我觉得我智商不只134，所以之前看到数字才不服气哪怕知道并不是智商测试，但是156对我来说又太高了。
我很努力地思考过，但还是没找到什么特别好的方法，除了识别一些基本的明显必然的情况外，我只能多练习，熟悉这种思维方式，就跟学下棋一样用练习来逐渐培养直觉。
感觉如果让计算机来解决靠穷举法就够快了，如果用计算机来穷举的话说不定还能看出一些更复杂的规律？反正我单看图是什么都看不出来，如果可以给图形进行变形的话，会轻松很多（本质不过是一些点和线，点的位置无关紧要，把所有点摆在一个圆上就不过是正多边形随机画了几条对角线而已）。或者明显必然的可以直接删除和简化，形状扭曲的可以模式化、编码和归类，不知道实际做起来怎么样，我只是这么想想。
不是很清楚作为世界难题真正要解决的是什么问题，在大学只学了一点数学。

**Developer response:** 可以换个帐号再做一遍，支持微博，QQ，苹果3种登录方式。当你做得快时，题目难度加快速度也会变快。我也想刷分，想刷个榜一，但把我的帐号都用完后，也只刷到了152。（建议先研究规律后，再刷一遍，看能不能突破154）

### 5/5 — 智力游戏

*2020-11-14*

挺好玩的，越玩越难，后面的关卡过不了

### 5/5 — 有点惭愧

*2020-09-15*

玩到70+关了，但是好像都是在凭着直觉划过去的关，然后感觉挺有意思的，但是自己思考的确实很少，有时候也有点像是在乱划，是数学专业的，以前借过图论的教材然后一开始被劝退了，最近又借了一本简单点的，希望能多了解一些内容以激发更强烈的兴趣，谢谢作者啦～
然后说一下可能存在的一个bug？玩完以后点击保存，会保存图片失败（听到音效但是没存上），（记得以前是可以保存的来着）

刚才通关了，智力才150😢

**Developer response:** 非常感谢你提出无法保存这一个问题，我们会尽快查明原因，并修复。

### 5/5 — Very good

*2020-09-05*

This is an interesting puzzle game.

### 1/5 — 不登陆没法玩

*2019-09-13*

玩个游戏还要获取社交账号信息，神烦

**Developer response:** 需要登录是为了不让用户好不容易测试的智力丢失了（如更换手机），新版本已经支持苹果登录——最安全的登录

### 4/5 — 这感觉像是在做数学题

*2018-08-26*

已通关.一开时凭眼力看路线的.后来直接变成数学题了，这个完整的回路有3个特征，1.过所有点.2.一个点冯管连着几根线，必然有且只有2条线是正确的.3.回路的每个点都可以当作起点，那么显然，只要1个点只有2条线那这2个线必然是属于正确路线的一部分，然后用排除法.和假设法.来判断.哪些线是迷惑你的，哪些线是正确的.感觉就是扫地雷吧，因为设计关卡，那证明必然有回路，其他再多的线都是迷惑，可能后面关卡大概就是平均每个点依次连着5.6根线把.没有2根线的正确信息，那样就是感觉像是玩捉迷藏了，只能用假设法来一点点排除，

**Developer response:** 你的评论很棒。你可以学习一下哈密顿图（离散数学）和NP完全问题（世界七大数学难题之一），对这个游戏会有更深刻的理解。

### 5/5 — 暂停计时

*2018-08-13*

挺好玩的，就是为什么暂停了还在计时？

**Developer response:** 为了防止做弊，以前暂停了是会停止计时的，但出现有些用户先截图然后暂停，然后通过截图解答关卡后，再回到游戏继续游戏并输入答案，导致其智力增长得特别快（过关用时少，智力增长就会快），最终测试的智力不准确。

## Frequently asked questions about Hamiltonian

### What is Hamiltonian?

Hamiltonian is an educational puzzle game where players must find a Hamiltonian circuit in a given graph. This involves visiting every vertex exactly once without repeating edges and returning to the starting vertex.

### What is the learning methodology of Hamiltonian?

Hamiltonian employs a challenge-based learning methodology. Players learn by solving increasingly difficult graph puzzles, which naturally enhances their problem-solving skills and logical thinking.

### How does Hamiltonian track progress?

Progress in Hamiltonian is tracked by the player's ability to complete levels. Each level represents a step up in difficulty, and successfully passing a level indicates mastery of that stage.

### Does Hamiltonian offer certifications?

Hamiltonian does not offer formal certifications. Its educational value lies in the inherent skill development gained through solving its complex graph puzzles.

### What is the price of Hamiltonian?

Hamiltonian is a paid app, available for $0.99. This one-time purchase grants access to all its features and content.

### On which devices can I play Hamiltonian?

Hamiltonian is compatible with iPhone, iPad, and iPod devices, offering a consistent experience across Apple's mobile ecosystem.

### How often is Hamiltonian updated?

Hamiltonian was last updated on December 3, 2020, with version 4.3.15. While updates may not be frequent, the core gameplay remains stable.

### What is the age rating for Hamiltonian?

Hamiltonian has an age rating of 4+, making it suitable for a wide range of younger and older players interested in logic and puzzles.

## Version history (last 5 releases)

### 4.3.15 — 2020-12-03

Bug fix

### 4.3.13 — 2020-11-19

Bug fix.

### 4.3.12 — 2020-11-14

Bug Fixes

### 4.3.11 — 2020-10-01

Bug Fixes

### 4.3.10 — 2020-09-29

Bug Fixes

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All apps by 奕鑫 史: https://appshunter.io/developer/1217732173

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*Data collected daily from the US App Store and indexed by [AppsHunter](https://appshunter.io/). User reviews are verbatim App Store reviews. Ratings, prices and chart positions refresh continuously; this snapshot is from 2026-08-24.*