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Problem londonskega stolpa [Elektronski vir]Meršak, InesProblem londonskega stolpa je miselna uganka; dane imamo palice določenih višin, na katerih so razporejene krogle različnih barv. Cilj igre je s čim manj premiki krogel preiti iz začetnega stanja v ... neko končno (dano) stanje krogel. Ker se londonski stolp pogosto uporablja za psihološka testiranja, v članku ta problem podrobneje preučimo: narišemo lahko graf, pri čemer so stanja krogel vozlišča, veljavne poteze pa povezave. Nato obravnavamo lastnosti tega grafa - najprej za klasični problem londonskega stolpa, kjer imamo 3 palice (višin 1, 2, 3) in 3 krogle različnih barv, nato pa še za splošen primer s p palicami in n kroglami. Izkaže se, da je graf klasičnega problema ravninski in vsebuje Hamiltonovo pot, ni pa Hamiltonov. Pri splošnem primeru dokažemo, da je graf nekega problema londonskega stolpa povezan natanko tedaj, ko lahko krogle razporedimo tako, da najvišja palica ostane prazna. Prav tako ugotovimo, da so ravninski le grafi problemov z dvema kroglama in nekateri grafi problemov s tremi kroglami. V članku obravnavamo tudi poseben primer londonskega stolpa, pri katerem so vse palice enake višine n, imenovan oxfordski stolp. Za tak problem izpeljemo formulo za število vozlišč in povezav za poljubna n in p.Source: Matrika [Elektronski vir] : izbrane teme sodobne fizike in matematike. - ISSN 2385-8567 (Letn. 3, št. 1, 2016, 13 str.)Type of material - e-articlePublish date - 2016Language - slovenianCOBISS.SI-ID - 2986852
Author
Meršak, Ines
Topics
matematika |
teorija grafov |
londonski stolp |
oxfordski stolp |
mathematics |
graph theory |
Tower of London |
Tower of Oxford
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