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 matches of B such that the number of pieces of bundles still form an arithmetic sequence. The player who cannot do a legal move loses. Determine which player has the winning strategy.


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

$X a n d Y a r e p l a y i n g a g a m e .$ $I n i t i a l l y t h e r e a r e t h r e e b u n d l e s o f$ $m a t c h e s, c o n s i s t i n g o f 2021, 2022$ $a n d 2023 p i e c e s . E a c h p l a y e r i n h i s$ $t u r n c h o o s e s a b u n d l e B a n d r e m o v e s$ $a p o s i t i v e n u m b e r o f t h e m a t c h e s o f B$ $s u c h t h a t t h e n u m b e r o f p i e c e s o f$ $b u n d l e s s t i l l f o r m a n a r i t h m e t i c$ $s e q u e n c e . T h e p l a y e r w h o c a n n o t d o a$ $l e g a l m o v e l o s e s . D e t e r m i n e w h i c h$ $p l a y e r h a s t h e w i n n i n g s t r a t e g y .$
Commented by LOSER last updated on 01/Oct/22

$I e d i t e d, s i r!$
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

$n o w m o r e c o n f u s i n g t h a n b e f o r e!$
Commented by Rasheed.Sindhi last updated on 01/Oct/22

$I f {y o u}^{'} v e t a k e n t h i s p r o b l e m f r o m$ $a b o o k, p l e a s e u p l o a d t h e i m a g e o f$ $t h e q u e s t i o n .$
Commented by peter frank last updated on 01/Oct/22

$hahahahah$
Commented by LOSER last updated on 02/Oct/22

$P l e a s e, h e l p m e! S o u r c e f r o m I C O .$
Commented by mr W last updated on 02/Oct/22

$q u e s t i o n p e r h a p s l i k e t h i s :$
Commented by mr W last updated on 02/Oct/22

$X a n d Y a r e p l a y i n g a g a m e .$ $I n i t i a l l y t h e r e a r e t h r e e b u n d l e s o f$ $m a t c h e s, c o n s i s t i n g o f 2021, 2022$ $a n d 2023 p i e c e s . E a c h p l a y e r i n h i s$ $t u r n c h o o s e s a b u n d l e a n d r e m o v e s$ $a p o s i t i v e n u m b e r o f m a t c h e s f r o m$ $t h i s b u n d l e s u c h t h a t t h e n u m b e r s o f$ $p i e c e s o f m a t c h e s i n t h e b u n d l e s s t i l l$ $f o r m a n a r i t h m e t i c s e q u e n c e . T h e$ $p l a y e r w h o c a n n o t d o a l e g a l m o v e$ $l o s e s . D e t e r m i n e w h i c h p l a y e r h a s$ $t h e w i n n i n g s t r a t e g y .$
Commented by LOSER last updated on 02/Oct/22

$Y e s i r!$
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