Question Number 177113 by LOSER last updated on 01/Oct/22
$${X}\:{and}\:{Y}\:{are}\:{playing}\:{a}\:{game}.\: \\ $$$${Initially}\:{there}\:{are}\:{three}\:{bundles}\:{of}\: \\ $$$${matches},\:{consisting}\:{of}\:\mathrm{2021},\:\mathrm{2022}\: \\ $$$${and}\:\mathrm{2023}\:{pieces}.\:{Each}\:{player}\:{in}\:{his}\: \\ $$$${turn}\:{chooses}\:{a}\:{bundle}\:{B}\:{and}\:{removes}\: \\ $$$${a}\:{positive}\:{number}\:{of}\:{the}\:{matches}\:{of}\:{B}\: \\ $$$${such}\:{that}\:{the}\:{number}\:{of}\:{pieces}\:{of}\: \\ $$$${bundles}\:{still}\:{form}\:{an}\:{arithmetic}\: \\ $$$${sequence}.\:{The}\:{player}\:{who}\:{cannot}\:{do}\:{a}\: \\ $$$${legal}\:{move}\:{loses}.\:{Determine}\:{which}\: \\ $$$${player}\:{has}\:{the}\:{winning}\:{strategy}. \\ $$
Commented by LOSER last updated on 01/Oct/22
$${I}\:{edited},\:{sir}! \\ $$
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
$${now}\:{more}\:{confusing}\:{than}\:{before}! \\ $$
Commented by Rasheed.Sindhi last updated on 01/Oct/22
$${If}\:\:{you}'{ve}\:{taken}\:{this}\:{problem}\:{from} \\ $$$${a}\:{book},\:{please}\:{upload}\:{the}\:{image}\:{of} \\ $$$${the}\:{question}. \\ $$
Commented by peter frank last updated on 01/Oct/22
$$\mathrm{hahahahah} \\ $$
Commented by LOSER last updated on 02/Oct/22
$${Please},\:{help}\:{me}!\:{Source}\:{from}\:{ICO}. \\ $$$$ \\ $$
Commented by mr W last updated on 02/Oct/22
$${question}\:{perhaps}\:{like}\:{this}: \\ $$
Commented by mr W last updated on 02/Oct/22
$${X}\:{and}\:{Y}\:{are}\:{playing}\:{a}\:{game}.\: \\ $$$${Initially}\:{there}\:{are}\:{three}\:{bundles}\:{of}\: \\ $$$${matches},\:{consisting}\:{of}\:\mathrm{2021},\:\mathrm{2022}\: \\ $$$${and}\:\mathrm{2023}\:{pieces}.\:{Each}\:{player}\:{in}\:{his}\: \\ $$$${turn}\:{chooses}\:{a}\:{bundle}\:{and}\:{removes}\: \\ $$$${a}\:{positive}\:{number}\:{of}\:\:{matches}\:{from} \\ $$$${this}\:{bundle}\:{such}\:{that}\:{the}\:{numbers}\:{of}\: \\ $$$${pieces}\:{of}\:{matches}\:{in}\:{the}\:{bundles}\:{still} \\ $$$${form}\:{an}\:{arithmetic}\:{sequence}.\:{The}\: \\ $$$${player}\:{who}\:{cannot}\:{do}\:{a}\:{legal}\:{move}\: \\ $$$${loses}.\:{Determine}\:{which}\:{player}\:{has}\: \\ $$$${the}\:{winning}\:{strategy}. \\ $$
Commented by LOSER last updated on 02/Oct/22
$${Ye}\:{sir}! \\ $$