# Echo Ramsey — Color graphs, advance a proof

> Color graphs, advance a proof (iPhone/iPad app by Sam Rostami.)

- Source: https://appshunter.io/ios/app/echo-ramsey/id6772779556 (this page in markdown: same URL + `.md`)
- Developer: [Sam Rostami](https://appshunter.io/developer/6771544652)
- Category: Games, Education, Puzzle
- Price: Free
- Age rating: 4+
- Requires: iOS 15.0 · 51 MB
- Languages: American English
- Released: 2026-06-05
- Data updated: 2026-08-13
- User reviews in markdown: https://appshunter.io/ios/app/echo-ramsey/id6772779556/reviews.md

## What is Echo Ramsey?

Echo is a puzzle game built on real open problems in mathematics.

  Each puzzle is a graph: dots joined by red and blue lines. Your job is simple to learn. Tap a line to flip its
  color, and break up the "bad cliques" - groups of dots all wired together in a single color. Clear them within your
  move budget and the puzzle is solved.

  Here is the twist. Every puzzle is a slice of a genuine research graph, and every solution you find is committed to
  a shared, growing proof tree. When you solve, your result seeds a brand new puzzle for another player. Their solve
  seeds the next. Together, the whole community is searching for colorings no person and no computer has ever found.

  You choose which problem to work on from the home screen:

  - R(4,4), the practice board - solved long ago, so the search genuinely finishes and you can see the whole engine
  work end to end
  - R(4,6), the frontier - an open problem where reaching zero would set a real new record
  - R(5,5), the legendary one - open for decades, where the prize is the lowest count the network has ever driven it
  to

  You do not need to know any of that to play. If you can spot a pattern and tap, you are already contributing.

  FEATURES

  - Quick, tactile puzzles you can finish in a minute
  - Three problems to play, from a winnable warm-up to a famous unsolved one, switchable any time
  - Five ways to view each graph: circle, spectral, matrix, hub, and density - switch any time to see the structure
  differently
  - A living progress screen showing the community's best reach and the proof tree growing in real time
  - Your lineage: see how many puzzles your solves have seeded for other players
  - A built-in glossary that explains every term in plain language
  - No ads, no timers, no pressure

  Color the graph. Advance the proof. Echo forward.


## Version history (last 4 releases)

### 1.0.5 — 2026-08-11

- A better onboarding.
- Small stability fixes.

### 1.0.2 — 2026-08-05

The tutorial no longer traps you. If a lesson has you stuck, you can now
skip it and carry on to the next one, or straight into a real puzzle.

Plus small stability fixes.

### 1.0.1 — 2026-06-26

The home "Every solve advances…" hint now opens the correct entry: on R(4,6) it shows "R(4,6) ≥ 37 … 36-dot graph … no red K₄ and no blue K₆," not the old R(5,5) description.

### 1.0 — 2026-06-05

No release notes.

## More apps by Sam Rostami

- [Coil Party](https://appshunter.io/ios/app/coil-party/id6771544650)
- [Bridges: Hashi Logic](https://appshunter.io/ios/app/bridges-hashi-logic/id6781868627)

All apps by Sam Rostami: https://appshunter.io/developer/6771544652

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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 2026-08-13.*