Finalist: Elias Lundheim

Elias Lundheim, 18 år, Trondheim
Skole: Trondheim Katedralskole

The random pawn game problem

Chess is a board game where pieces on a board follow simple rules, and two players use these pieces to capture the opponent’s king. In addition to this traditional game, there have also been countless problems like the Knight’s Tour or the Eight Queens Puzzle. While many of these have been solved, some remain unsolved, where the answers are hidden behind a vast number of calculations. One of these problems is to find the number of unique chess games. One of the first to provide an estimate of this number was Claude Shannon who claimed in his 1950 paper "Programming a computer for playing chess" that the number would be about 1043, but many have come closer today.

I have had an interest for chess for a long time, and the idea of making a system of rules and values interacting with one another has always been intriguing. In my paper, I discuss one such system, and try to solve one problem within this system. I start with traditional chess as my frame, and add or remove move elements I want or do not want to be a part of my system. What I end up with is my own game which moves and behaves quite differently from traditional chess. It might be a bit of a stretch to even call it a game, since it does not have an end goal. None the less, the idea of making simple rules that create complicated scenarios is a passion for me. (Langton’s Ant is a great example of this.)

My initial thought for a problem was a quite practical one; If you throw some pieces onto a chess board, would two players be able to reach that position, starting from a standard board? What would be the likelihood of such a random board occurring? Calculating this for a full board would be nearly impossible with our current methods and computing power since you end up having to find all possible chess games, but I still wanted to explore the problem. To do this, I started at a much simpler level, with only pawns and a smaller board. My essay explores different ways of calculating this probability, and discusses various problems concerning the task.



Related news

Latest news

Great interest in smart options

An increasing number of people become aware of how smart options can make the construction process more efficient and life for residents easier, says product manager NorDan Smart, Olav Hjørungnes.

Salmon Wellboat Sails Electric

The new MS SEIHAV has now gone on chart with the Norwegian salmon farming company Lerøy Seafood Group. A reliable and environmentally sustainable propulsion arrangement has been chosen for MS SEIHAV.

Servogear at Interferry 2016

It is almost time for the 41th annual Interferry Conference. From October 15-19, Servogear will be present in Manila.

Strainstall mooring monitoring for Hywind

Strainstall provides specialised mooring monitoring for pioneering floating offshore wind farm project, Hywind. Collaboration with MacGregor delivers fully integrated mooring solution to monitor the forces on the floating ...

NSM Signs contract with Embraer

Norwegian Special Mission signed a contract with Embraer to supply six (6) UNIFIS 3000 Navaids Flight Inspection Systems to be integrated into six Embraer Legacy 500 aircraft.

Designing the energy solutions for autonomous airships

The Stratobus project is a new concept for an autonomous airship, operating at an altitude of about 20 kilometers. It is led by Thales Alenia Space (TAS). CMR Prototech has been chosen by Thales Alenia Space to s...

Expanded collaboration with DNV GL - Business Assurance

Steinsvik and DNV GL - Business Assurance have signed a framework agreement on product certification of barges for aquaculture.

"Maud" Returns Home

CMR had two men working on the research ship "Maud", Harald Ulrik Sverdrup and Odd Dahl. Both helped Roald Amundsen to get his project through and this highly scientific expedition could be realized. Sverdrup was scientifi...

The impact of NORCOWE

"NORCOWE has been instrumental for StormGeo’s positioning in the [offshore wind] market, " StormGeo’s vice president Renewables Jostein Mælan declared at NORCOWE 2016.