Pegs, Pebbles, Pennies and Piles — a study of some combinatorial games
Niklas Eriksen · 1999
In this master’s thesis, I will discuss some aspects of four combinatorial games. These are Pegs (also known as solitaire), Pebbles, Pennies and Piles, which are described in this report. The main contents can be summarised as follows. • Already known results for Pegs, Pebbles and Piles, together with the standard techniques. • A study of Pennies, which is an entirely new game. On most boards, Pennies is not solvable. • The reachable area of Pegs in Z, allowing diagonal moves, has been investigated. I have found that there still is a rather narrow limit on how far one can reach, but it is substantially larger than the limit obtained not allowing diagonal moves. • The solvability of Pegs on some unconventional boards has been investigated. I have also obtained some results on the solvability of a game using a kind of sideways Pegs move. Sammanfattning Denna examensarbetesrapport behandlar fyra kombinatoriska spel. Dessa ar Pegs (aven kant som solitaire), Pebbles, Pennies och Piles, vilka beskrivs i rapporten. De viktigaste amnena som behandlas ar foljande. • En genomgang av redan kanda resultat for Pegs, Pebbles och Piles, samt de standardtekniker som anvands. • Det helt nya spelet Pennies presenteras. Pa de flesta braden saknar Pennies losning. • Rackvidden for Pegs i Z, om vi tillater diagonala drag, har undersokts. Vi finner rackvidden ar langre an i vanligt Pegs, d.v.s. utan diagonala drag, men anda starkt begransad. • Losbarheten for Pegs pa en del ovanliga braden har undersokts. Jag har aven undersokt losbarheten for det spel som fas, da man anvander en sidledesvariant av dragen i Pegs.