Stomp combined
- 1. StompingonDots
Activity
AStomppuzzleconsistsofarectangularboardmadeupofunitsquares,asmaller"Stomppiece"
alsomadeupofunitsquares,andsomeinitialconfigurationofdotsappearingontheStomp
boardwithatmostonedotperunitsquare.YouareallowedtoplacetheStomppieceanywhere
withinthegridoneachmove,aslongasitlinesupwiththegridandstayswithintheboundary.
Allthesquaresthatarecoveredthenchangestate,sothatdotsthatarecovereddisappear,while
emptysquaresthatarecoveredsproutnewdots.Thegoalistoobliterateallthedotsinasfew
movesaspossible,ortoprovethatitisimpossibletodoso.
Questions
1.FindawaytoclearthetopleftStompboardinasfewmovesaspossible,usingtheshortL-
triominototherightoftheboardasyourStomppiece.
2.FindawaytoclearthetoprightStompboardinasfewmovesaspossible,usingthelongL-
tetrominopicturednexttotheboard.
3.IsitpossibletoclearthetopmiddleStompboardusingtheT-tetrominoshowntotherightof
theboard?Ifso,doitinasfewmovesaspossible;ifnot,explainwhyitisimpossible.
4.IsitpossibletoclearthebottomleftStompboardusingthedominoshowntotherightofthe
board?Ifso,doitinasfewmovesaspossible;ifnot,explainwhyitisimpossible.
5.ProvethatitisimpossibletoclearthebottomrightStompboardwiththeI-triominoshown
nexttotheboard.
6.Supposethatyouaregivenarectangularboardwhoselengthandwidthareeachatleastfour,
withanyinitialarrangementofdots.Explainwhyitisalwayspossibletocleartheboardusing
anL-triomino(thetopleftboardStomppiece).
7.OnceagainimaginethatyouareplayingStomponarectangularboardwhoselengthand
widthareeachatleastfour.Provethatiftwodotsareinitiallyplacedinanytwosquares,thenit
ispossibletocleartheboardusingtheT-tetromino(thetopmiddleboardStomppiece).