# An ancient, complex game examined

##### March 29, 2011

North Dakota State University mathematics doctoral student Lindsay (Merchant) Erickson is fascinated by the ancient game of Nim. A two-player pastime of combinatorial game theory, Nim's origins date hundreds of years ago in China.

"Nim is a game of perfect information, meaning that both players know what their opponent is doing at every step, and there are no elements of chance involved," Erickson explained, noting there is only one solution to the general game.

"Nim's not as difficult as mathematicians would like you to believe - I've taught the game to third graders. In fact, the only person to ever beat me in the general game of Nim is a third grader," said Erickson, who earned her bachelor's degree in at NDSU in 2006.

Now, Erickson has taken the game in a new direction, using graphs so the solution of the general game does not apply. Erickson's 60-page doctoral dissertation, "The Game of Nim on Graphs," demonstrates different solutions are dependent on the structure of the graphs. It's an intricate study of the complex game, with the goal to discover winning strategies and predict who will be the victor.

In her work, she extended the game to mathematical graphs such as complete graphs, Petersen graphs, hypercubes and bipartite graphs. Erickson assigned integer weight to each edge from a given vertex to correspond to the pile of stones used in an ordinary of Nim. She took into account nearly every possible move and ended up putting her supporting materials on a CD, because the graphs would have filled a 2,000-page appendix.

An outstanding student, Erickson has received three National Science Foundation fellowships, a dissertation fellowship through the Graduate School and numerous scholarships. She also studied mathematics one summer in Hungary.

"So often I'm told, 'Oh, my gosh, you're getting a Ph.D. in math. You must be so smart,' " she said with a laugh. "Well, I'm good at math, but don't expect me to write an English paper. It's not going to happen."

A native of Moorhead, Erickson will earn her doctorate in May. She hopes to find a post-doctoral position and eventually work at a research university.

As she nears graduation, she feels NDSU has prepared her well. "The faculty of my department have worked quite a bit in the last few years at implementing new programs and seminars to help students prepare to enter the work force. We are encouraged to attend conferences and give talks, as well as teach our own courses whenever possible. All of these areas are significant to the work we will do post‑graduation."

Explore further: Undergrad student creates word-based game for iPhone

## Related Stories

#### Undergrad student creates word-based game for iPhone

January 14, 2011

(PhysOrg.com) -- A recently released iPhone and iPad application may seem like a challenging word game for most. But to one undergraduate student in the Department of Electrical and Computer Engineering at Texas A&M University, ...

#### Briefs: Nintendo to launch new Pokemon game

January 5, 2006

Nintendo said Thursday it will launch a new Pokemon game on March 6.

#### Degree offered in computer game design

July 12, 2006

The University of California-Santa Cruz has approved a new science major in computer game design.

#### 8 percent of fans legally drunk after attending professional sports games

January 18, 2011

It's no secret that there is a lot of alcohol consumed by fans at sporting events, but is it possible to measure the blood alcohol content (BAC) of fans as they exit the stadiums? And if BAC levels can be measured, what do ...

#### Company pulls plug on 'Fallujah' video game

April 28, 2009

(AP) -- The publisher behind a video game based on one of the Iraq war's fiercest battles has pulled the plug on the title, called "Six Days in Fallujah."

#### Stanford mathematician: In reality, simulation is key to math education

February 22, 2010

(PhysOrg.com) -- Role-playing games such as "World of Warcraft" could reverse the declining math proficiency of middle school students, Keith Devlin told an audience at the AAAS annual meeting in San Diego.

## Recommended for you

#### Ancient fish scales and vertebrate teeth share an embryonic origin

November 20, 2017

In biology, one long-running debate has teeth: whether ancient fish scales moved into the mouth with the origin of jaws, or if the tooth had its own evolutionary inception.

#### New paper answers causation conundrum

November 17, 2017

In a new paper published in a special issue of theÂ Philosophical Transactions of the Royal Society A, SFI Professor Jessica Flack offers a practical answer to one of the most significant, and most confused questions in evolutionary ...

#### Study refutes theory linking cognition, genes and income

November 17, 2017

Researchers have cast doubt on a widely-held belief that connects family income with cognitive development, according to a new study published in Proceedings of the National Academy of Sciences.

#### Mathematician's study of 'swarmalators' could direct future science

November 17, 2017

How does the Japanese tree frog figure into the latest work of noted mathematician Steven Strogatz? As it turns out, quite prominently.

#### Fossil that fills missing evolutionary link named after University of Chicago professors

November 17, 2017

Lurking in oceans, rivers and lakes around the world are tiny, ancient animals known to few people. Bryozoans, tiny marine creatures that live in colonies, are "living fossils"â€”their lineage goes back to the time when multi-celled ...

#### Chance discovery of forgotten 1960s 'preprint' experiment

November 16, 2017

For years, scientists have complained that it can take months or even years for a scientific discovery to be published, because of the slowness of peer review. To cut through this problem, researchers in physics and mathematics ...

Mar 29, 2011
This comment has been removed by a moderator.
##### trekgeek1
5 / 5 (6) Mar 29, 2011
-A physicist, an engineer and a statistician are hunting. The three of them see a deer. The physicist performs a calculation for trajectory, neglecting air resistance. His shot falls 5 meters short. The engineer sees this and slightly lifts the barrel of the gun to compensate. He shoots and the shot goes 5 meters too far. The statistician yells "We got 'em"!

- A physicist, and engineer and a mathematician are sleeping in a hotel. A fire starts in the physicists room. He wakes, calculates the exact volume of water needed to extinguish the flame, fills a graduated cylinder and pours the water on the flame. Same thing happens to the engineer, he wakes, fills a bucket with water and douses the flame,soaking the room. Next, a fire starts in the mathematicians room. He wakes, begins calculations, proves that the fire can be extinguished and then goes back to bed.

Practical application rules! :p
##### jjoensuu
not rated yet Mar 30, 2011
Nimphomaniac.

Why you say that for? Just because the lady looks cute?
##### Doug_Huffman
not rated yet Mar 31, 2011
Nimphomaniac.

Why you say that for? Just because the lady looks cute?
Nim-phomaniac, maybe maniac-pho-nim will be clearer. Joe-n-Sue? Or cainamohpmiN cainam ohp miN?