Question Number 153458 by liberty last updated on 07/Sep/21
$${Given}\:{a}\:{set}\:{consisting}\:{of}\:\mathrm{22}\:{integer} \\ $$$$\:{A}=\left\{\pm{a}_{\mathrm{1}} ,\pm{a}_{\mathrm{2}} ,...,\pm{a}_{\mathrm{11}} \right\}.\:{Show}\:{that} \\ $$$${exist}\:{subset}\:{of}\:{S}\:{with}\:{properties} \\ $$$$\left(\mathrm{1}\right)\:{for}\:{every}\:{i}=\mathrm{1},\mathrm{2},\mathrm{3},...,\mathrm{11}\: \\ $$$$\:{have}\:{least}\:{one}\:{between}\:{a}_{{i}} \:{or}\:−{a}_{{i}} \\ $$$$\:{element}\:{of}\:{S} \\ $$$$\left(\mathrm{2}\right){the}\:{sum}\:{all}\:{possible}\:{numbers} \\ $$$${in}\:{S}\:{divisible}\:{by}\:\mathrm{2015} \\ $$
Commented by talminator2856791 last updated on 07/Sep/21
$$\:\mathrm{please}\:\mathrm{phrase}\:\mathrm{the}\:\mathrm{question}\:\mathrm{better}. \\ $$