Question Number 192856 by universe last updated on 29/May/23
$$\:{if}\:{a}+{b}+{c}\:+{d}\:\:=\:\mathrm{63}\:{and}\:{a},{b},{c},{d}\:\in\:\mathbb{N}\:{find}\: \\ $$$$\:\:\:{the}\:{maximum}\:{value}\:{of}\:{ab}+{bc}+{cd}\:=\:? \\ $$
Answered by Frix last updated on 29/May/23
$$\mathrm{32}+\mathrm{31}+\mathrm{0}+\mathrm{0}=\mathrm{63} \\ $$$$\mathrm{32}×\mathrm{31}=\mathrm{992} \\ $$
Commented by AST last updated on 30/May/23
Commented by AST last updated on 30/May/23
$${If}\:{N}^{\ast} ,{then}\:\mathrm{991}.\:{But}\:{if}\:{N}_{\mathrm{0}} ,{then}\:\mathrm{992}. \\ $$
Commented by AST last updated on 30/May/23
$${a},{b},{c},{d}\in\mathbb{N},\:\mathrm{0}\notin\mathbb{N}\left({by}\:{definition}\right) \\ $$
Commented by Frix last updated on 30/May/23
$$\mathrm{Some}\:\mathrm{define} \\ $$$$\mathbb{N}=\left\{\mathrm{0},\:\mathrm{1},\:\mathrm{2},\:\mathrm{3},\:…\right\}\:\mathrm{and}\:\mathbb{N}^{\bigstar} =\mathbb{N}\backslash\left\{\mathrm{0}\right\} \\ $$$$\mathrm{others} \\ $$$$\mathbb{N}=\left\{\mathrm{1},\:\mathrm{2},\:\mathrm{3},\:\mathrm{4},\:…\right\}\:\mathrm{and}\:\mathbb{N}_{\mathrm{0}} =\mathbb{N}\cup\left\{\mathrm{0}\right\} \\ $$$$\mathrm{It}\:\mathrm{had}\:\mathrm{been}\:\mathrm{dicussed}\:\mathrm{here}\:\mathrm{several}\:\mathrm{times} \\ $$$$\mathrm{before}. \\ $$
Commented by Frix last updated on 30/May/23
$$\mathrm{Yes}. \\ $$
Answered by nikif99 last updated on 30/May/23
$${if}\:\mathbb{N}^{\ast} \:{then}\:\left({a},{b},{c},{d}\right)=\left(\mathrm{1},\mathrm{31},\mathrm{30},\mathrm{1}\right)\:{or} \\ $$$$\left(\mathrm{1},\mathrm{30},\mathrm{31},\mathrm{1}\right),\:{with}\:{max}=\mathrm{991}. \\ $$