TOWER 1 to TOWER 2 under the following

ThepuzzleoftheTowerofHanoiistomoveallofthediscsfromTOWER 1 toTOWER 2 underthefollowingrestrictions:1–Oneachmovetransferonediscfromthetopofanytowertoanothertower.2–Atilemayonlygoontopofalargertile.Thechallengeistomovetheentiretowerinthefewestpossiblemoves.OBSERVATIONS:Thefewestnumberofmovestomoveatowerof2discsappearstobe7.Andthefewestmovestomoveatowerofthreediscsappearstobe15.Wecametotheseconclusionsbyexperimenting.Toanalyzethesitutationfurtherwedisplayedallpossible(legal)configurationsforjusttwodiscs.Seeattachedpage.Arrangingtheseconfigurationsintoavertex‐edgegraph,wewereabletoseetheshortestpathfromtheinitialpositiontothedesiredconfigurationisindeedjust7steps.Wewanttocontinuetheinvestigationbydoingthesameforthreediscs.CONNECTIONTO1213Bonnieshowedhowtosolvethepuzzleusing1213sequence.Forthismethodthediscsneedarrowspointingtotheleftorrightalternatelyupthetower.ThearrowonthebottomtowershouldpointtoTOWER 2. Furtherwelabelthetowersinorderoflength1,2,3,4,5,6,7,8,9,...asneeded.Tomovethediscsmovetheminorderofthe1213sequence.Moveeachdiscinthedirectionofit’sarrow.Ifthereisn’tatowerinthatdirection,wraparoundtothetowerontheotherend.Whydoesthiswork?