Question Number 57513 by pete last updated on 06/Apr/19
$$\mathrm{There}\:\mathrm{are}\:\mathrm{128}\:\mathrm{players}\:\mathrm{in}\:\mathrm{the}\:\mathrm{first}\:\mathrm{round} \\ $$$$\mathrm{of}\:\mathrm{a}\:\mathrm{knockout}\:\mathrm{competition}.\:\mathrm{Half}\:\mathrm{of}\:\mathrm{the} \\ $$$$\mathrm{players}\:\mathrm{were}\:\mathrm{knocked}\:\mathrm{out}\:\mathrm{in}\:\mathrm{each}\:\mathrm{round}. \\ $$$$\mathrm{How}\:\mathrm{many}\:\mathrm{players}\:\mathrm{took}\:\mathrm{part}\:\mathrm{in}\:\mathrm{the} \\ $$$$\mathrm{fourth}\:\mathrm{round}?\:\mathrm{How}\:\mathrm{many}\:\mathrm{rounds}\:\mathrm{were}\:\mathrm{there} \\ $$$$\mathrm{in}\:\mathrm{this}\:\mathrm{competion}? \\ $$
Commented by mr W last updated on 06/Apr/19
$$\mathrm{1}{st}\:{round}:\:\mathrm{128}\rightarrow\mathrm{64} \\ $$$$\mathrm{2}{nd}\:{round}:\:\mathrm{64}\rightarrow\mathrm{32} \\ $$$$\mathrm{3}{rd}\:{round}:\:\mathrm{32}\rightarrow\mathrm{16} \\ $$$$\mathrm{4}{th}\:{round}:\:\mathrm{16}\rightarrow\mathrm{8} \\ $$$$\mathrm{5}{th}\:{round}:\:\mathrm{8}\rightarrow\mathrm{4} \\ $$$$\mathrm{6}{th}\:{round}:\:\mathrm{4}\rightarrow\mathrm{2} \\ $$$$\mathrm{7}{th}\:{round}:\:\mathrm{2}\rightarrow\mathrm{1} \\ $$$$ \\ $$$$\Rightarrow\mathrm{16}\:{players}\:{took}\:{part}\:{in}\:\mathrm{4}{th}\:{round}, \\ $$$${there}\:{were}\:\mathrm{7}\:{rounds}. \\ $$
Commented by pete last updated on 06/Apr/19
$$\mathrm{Thank}\:\mathrm{you}\:\mathrm{sir} \\ $$
Commented by rahul 19 last updated on 06/Apr/19
$$\left({b}\right)\:\mathrm{2}^{{x}} =\mathrm{128}\:\Rightarrow{x}=\mathrm{7}\:{rounds}. \\ $$
Commented by tanmay.chaudhury50@gmail.com last updated on 06/Apr/19
$${Rahul}\:...{you}\:{pls}\:{feed}\:{problems}\:{in}\:{the}\:{forum}.. \\ $$$${we}\:{are}\:{starved}\:...{feedind}\:{is}\:{less}\:{so}\:{forum}\:{is}\:{getting} \\ $$$${slowed}\:{down}... \\ $$