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

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.

$${X}\:{and}\:{Y}\:{are}\:{playing}\:{a}\:{game}.\: \\ $$$${Initially}\:{there}\:{are}\:{three}\:{bundles}\:{of}\: \\ $$$${matches},\:{consisting}\:{of}\:\mathrm{2021},\:\mathrm{2022}\: \\ $$$${and}\:\mathrm{2023}\:{pieces}.\:{Each}\:{player}\:{in}\:{his}\: \\ $$$${turn}\:{chooses}\:{a}\:{bundle}\:{B}\:{and}\:{removes}\: \\ $$$${a}\:{positive}\:{number}\:{of}\:{the}\:{matches}\:{of}\:{B}\: \\ $$$${such}\:{that}\:{the}\:{number}\:{of}\:{pieces}\:{of}\: \\ $$$${bundles}\:{still}\:{form}\:{an}\:{arithmetic}\: \\ $$$${sequence}.\:{The}\:{player}\:{who}\:{cannot}\:{do}\:{a}\: \\ $$$${legal}\:{move}\:{loses}.\:{Determine}\:{which}\: \\ $$$${player}\:{has}\:{the}\:{winning}\:{strategy}. \\ $$

Commented by LOSER last updated on 01/Oct/22

I edited, sir!

$${I}\:{edited},\:{sir}! \\ $$

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

now more confusing than before!

$${now}\:{more}\:{confusing}\:{than}\:{before}! \\ $$

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

If you′ve taken this problem from a book, please upload the image of the question.

$${If}\:\:{you}'{ve}\:{taken}\:{this}\:{problem}\:{from} \\ $$$${a}\:{book},\:{please}\:{upload}\:{the}\:{image}\:{of} \\ $$$${the}\:{question}. \\ $$

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

hahahahah

$$\mathrm{hahahahah} \\ $$

Commented by LOSER last updated on 02/Oct/22

Please, help me! Source from ICO.

$${Please},\:{help}\:{me}!\:{Source}\:{from}\:{ICO}. \\ $$$$ \\ $$

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

question perhaps like this:

$${question}\:{perhaps}\:{like}\:{this}: \\ $$

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

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 and removes a positive number of matches from this bundle such that the numbers of pieces of matches in the bundles still form an arithmetic sequence. The player who cannot do a legal move loses. Determine which player has the winning strategy.

$${X}\:{and}\:{Y}\:{are}\:{playing}\:{a}\:{game}.\: \\ $$$${Initially}\:{there}\:{are}\:{three}\:{bundles}\:{of}\: \\ $$$${matches},\:{consisting}\:{of}\:\mathrm{2021},\:\mathrm{2022}\: \\ $$$${and}\:\mathrm{2023}\:{pieces}.\:{Each}\:{player}\:{in}\:{his}\: \\ $$$${turn}\:{chooses}\:{a}\:{bundle}\:{and}\:{removes}\: \\ $$$${a}\:{positive}\:{number}\:{of}\:\:{matches}\:{from} \\ $$$${this}\:{bundle}\:{such}\:{that}\:{the}\:{numbers}\:{of}\: \\ $$$${pieces}\:{of}\:{matches}\:{in}\:{the}\:{bundles}\:{still} \\ $$$${form}\:{an}\:{arithmetic}\:{sequence}.\:{The}\: \\ $$$${player}\:{who}\:{cannot}\:{do}\:{a}\:{legal}\:{move}\: \\ $$$${loses}.\:{Determine}\:{which}\:{player}\:{has}\: \\ $$$${the}\:{winning}\:{strategy}. \\ $$

Commented by LOSER last updated on 02/Oct/22

Ye sir!

$${Ye}\:{sir}! \\ $$

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