Question Number 112531 by Aina Samuel Temidayo last updated on 08/Sep/20
$$\mathrm{A}\:\mathrm{rectangular}\:\mathrm{cardboard}\:\mathrm{is}\:\mathrm{8cm}\:\mathrm{long} \\ $$$$\mathrm{and}\:\mathrm{6cm}\:\mathrm{wide}.\:\mathrm{What}\:\mathrm{is}\:\mathrm{the}\:\mathrm{least} \\ $$$$\mathrm{number}\:\mathrm{of}\:\mathrm{beads}\:\mathrm{you}\:\mathrm{can}\:\mathrm{arrange}\:\mathrm{on} \\ $$$$\mathrm{the}\:\mathrm{board}\:\mathrm{such}\:\mathrm{that}\:\mathrm{there}\:\mathrm{are}\:\mathrm{at}\:\mathrm{least} \\ $$$$\mathrm{two}\:\mathrm{of}\:\mathrm{the}\:\mathrm{beads}\:\mathrm{that}\:\mathrm{are}\:\mathrm{less}\:\mathrm{than} \\ $$$$\sqrt{\mathrm{10}}\mathrm{cm}\:\mathrm{apart}. \\ $$
Commented by mr W last updated on 08/Sep/20
$${the}\:{question}\:{is}\:{not}\:{clear}. \\ $$$${for}\:{me}\:{we}\:{only}\:{need}\:{to}\:{put}\:{two} \\ $$$${beads}\:{on}\:{board}\:{with}\:{a}\:{distance}\:<\sqrt{\mathrm{10}}. \\ $$
Commented by Aina Samuel Temidayo last updated on 09/Sep/20
$$\mathrm{I}\:\mathrm{don}'\mathrm{t}\:\mathrm{think}\:\mathrm{so}. \\ $$
Commented by mr W last updated on 09/Sep/20
$${i}\:{understand}\:{the}\:{question}\:{now}. \\ $$$${the}\:{question}\:{is}\:{how}\:{many}\:{breads}\:{can} \\ $$$${you}\:{maximally}\:{place}\:{on}\:{the}\:{table} \\ $$$${such}\:{that}\:{the}\:{distances}\:{between}\:{them} \\ $$$${are}\:{not}\:{less}\:{than}\:\sqrt{\mathrm{10}}.\:{answer}\:{should} \\ $$$${be}\:{easy}. \\ $$
Commented by Aina Samuel Temidayo last updated on 09/Sep/20
$$\mathrm{Ok}.\:\mathrm{Please}\:\mathrm{solve}. \\ $$