X-and-Y-are-playing-a-game-Initially-there-are-three-bundles-of-matches-consisting-of-2021-2022-and-2023-pieces-Each-player-in-his-turn-chooses-a-bundle-B-and-removes-a-positive-number-of-the

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Question Number 177113 by LOSER last updated on 01/Oct/22

$$XandYareplayingagame.$$$$Initiallytherearethreebundlesof$$$$matches,consistingof2021,2022$$$$and2023pieces.Eachplayerinhis$$$$turnchoosesabundleBandremoves$$$$apositivenumberofthematchesofB$$$$suchthatthenumberofpiecesof$$$$bundlesstillformanarithmetic$$$$sequence.Theplayerwhocannotdoa$$$$legalmoveloses.Determinewhich$$$$playerhasthewinningstrategy.$$

Commented by LOSER last updated on 01/Oct/22

$$Iedited,sir!$$

Commented by JDamian last updated on 01/Oct/22

it is confusing. You call a player B and later, you say "a bundle B" and "the matches of B". What is B?

Commented by mr W last updated on 01/Oct/22

$$nowmoreconfusingthanbefore!$$

Commented by Rasheed.Sindhi last updated on 01/Oct/22

$$If{you}^{\prime }vetakenthisproblemfrom$$$$abook,pleaseuploadtheimageof$$$$thequestion.$$

Commented by peter frank last updated on 01/Oct/22

$$\mathrm{hahahahah}$$

Commented by LOSER last updated on 02/Oct/22

$$Please,helpme!SourcefromICO.$$$$$$

Commented by mr W last updated on 02/Oct/22

$$questionperhapslikethis:$$

Commented by mr W last updated on 02/Oct/22

$$XandYareplayingagame.$$$$Initiallytherearethreebundlesof$$$$matches,consistingof2021,2022$$$$and2023pieces.Eachplayerinhis$$$$turnchoosesabundleandremoves$$$$apositivenumberofmatchesfrom$$$$thisbundlesuchthatthenumbersof$$$$piecesofmatchesinthebundlesstill$$$$formanarithmeticsequence.The$$$$playerwhocannotdoalegalmove$$$$loses.Determinewhichplayerhas$$$$thewinningstrategy.$$

Commented by LOSER last updated on 02/Oct/22

$$Yesir!$$

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