In-a-room-containing-N-people-N-gt-3-at-least-one-person-has-not-shaken-hands-with-everyone-else-in-the-room-What-is-the-maximum-number-of-people-in-the-room-that-could-have-shaken-hands-with-ev

Question Number 125460 by john_santu last updated on 11/Dec/20

$$\:{In}\:{a}\:{room}\:{containing}\:{N}\:{people} \\ $$$${N}>\mathrm{3},\:{at}\:{least}\:{one}\:{person}\:{has}\:{not} \\ $$$${shaken}\:{hands}\:{with}\:{everyone} \\ $$$${else}\:{in}\:{the}\:{room}.\:{What}\:{is}\:{the}\: \\ $$$${maximum}\:{number}\:{of}\:{people}\: \\ $$$${in}\:{the}\:{room}\:{that}\:{could}\:{have}\: \\ $$$${shaken}\:{hands}\:{with}\:{everyone}\: \\ $$$${else}?\: \\ $$

Answered by liberty last updated on 11/Dec/20

$${N}−\mathrm{2} \\ $$

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