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# GOODTHINKINGGAMES

##### Original, fun, free, challenging puzzle games for persistent solvers.

The Hamiltonian Circuit

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#### GAMES

##### THE HAMILTONIAN CIRCUIT

Inspired by a game designed by Irish mathematician Sir William Rowan Hamilton in 1859, The Hamiltonian Circuit is based on graph theory. Think of it as a giant maze. To create the circuit, you have to visit each vertex in the grid exactly once, never going backward or crossing the path or a wall. There is only one solution per circuit.

For more specific information on how to tackle these puzzles, see our Solving Tips.

## William Rowan Hamilton

On October 16, 1843, when Hamilton was considering ways to extend complex numbers to higher spatial dimensions, he began working in four dimensions, and in doing so, discovered quaternions. The actual equation came to him at an inopportune time; he was walking along the Royal Canal in Dublin with his wife, and with nothing else to write on, he took out his penknife and carved it into the side of the nearby Broom Bridge. Although his original carving is gone, this plaque was placed there in his honor on November 13, 1953 by Taoiseach Eamon de Valera, a mathematician and student of quaternions.

## Solving Tips

How to become an expert solver

## 4

01

### Look for corners

Some grid cells have only two sides open due to walls or the edge of the grid. Filling these in first will get you a long way toward solving the puzzle.

02

### Avoid loops

While you must complete one big loop to solve the puzzle, no loops that are smaller than the entire puzzle are allowed. Sometimes you can find a place where the path has to go to avoid creating a loop.

03

### Everything is connected

Because the solution path is a single path that goes everywhere, each part of the path has to connect to the rest of the puzzle. That means that if you see an area with only two possible paths in and out, you can fill them in.

04

### Use pencil mode and hints

Pencil mode gives you a way to try out an idea. If it isn't working out, canceling pencil mode will take you back to exactly what you had before you entered pencil mode. If it looks good, you can commit all of your pencil marks. Using a hint will tell you if you're on the right track. If you have any mistakes, the hint will remove an erroneous segment and highlight it in red. If not, you'll see a segment added with green highlighting.

### WE ARE

Good Thinking Games Ltd is dedicated to making fun, stimulating puzzle games inspired by recreational mathematics and language. One of the founders is a mathematician who worked at the highest levels in the world's most successful software companies; the other is a total mathphobe who worked on the creative end at some of the very same companies. Now we've combined our experience with our passion to create great original games. When we're not solving puzzles, we're traipsing about with our greyhound, 99.