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Question Number 113353 by Aina Samuel Temidayo last updated on 12/Sep/20
$$\mathrm{What}\:\mathrm{is}\:\mathrm{the}\:\mathrm{maximum}\:\mathrm{number} \\ $$$$\mathrm{of}\:\mathrm{points}\:\mathrm{to}\:\mathrm{be}\:\mathrm{distributed}\:\mathrm{within} \\ $$$$\mathrm{a}\:\mathrm{3}×\mathrm{6}\:\mathrm{to}\:\mathrm{ensure}\:\mathrm{that}\:\mathrm{there}\:\mathrm{are}\:\mathrm{no}\:\mathrm{two} \\ $$$$\mathrm{points}\:\mathrm{whose}\:\mathrm{distance}\:\mathrm{apart}\:\mathrm{is}\:\mathrm{less} \\ $$$$\mathrm{than}\:\sqrt{\mathrm{2}}? \\ $$
Answered by mr W last updated on 13/Sep/20
Commented by mr W last updated on 13/Sep/20
Commented by mr W last updated on 13/Sep/20
$${points}\:{on}\:{grid}\:\sqrt{\mathrm{2}} \\ $$$${board}\:\mathrm{3}×\mathrm{6}\:{can}\:{cover}\:{at}\:{most}\:\mathrm{13}\:{points}. \\ $$$${i}.{e}.\:{one}\:{can}\:{put}\:{at}\:{most}\:\mathrm{13}\:{points} \\ $$$${such}\:{that}\:{no}\:{two}\:{points}\:{are}\:{not}\:{less} \\ $$$${than}\:\sqrt{\mathrm{2}}\:{apart}. \\ $$
Commented by Aina Samuel Temidayo last updated on 13/Sep/20
$$\mathrm{Thanks}. \\ $$