Question Number 6464 by nburiburu last updated on 27/Jun/16
$$``{In}\:{a}\:{great}\:{reunion}\:{each}\:{person}\:{knows} \\ $$$${at}\:{least}\:{two}\:{different}\:{persons}\:{in}\:{there}''.\:{Show}\: \\ $$$${that}\:{this}\:{statement}\:{implies}\:{that}\:{exists} \\ $$$${one}\:{person}\:{who}\:{has}\:{to}\:{know}\:{everyone}. \\ $$
Commented by prakash jain last updated on 27/Jun/16
$$\mathrm{1}\:\mathrm{knows}\:\mathrm{2}\:\mathrm{3} \\ $$$$\mathrm{2}\:\mathrm{knows}\:\mathrm{3}\:\mathrm{4} \\ $$$$\mathrm{and}\:\mathrm{so}\:\mathrm{on} \\ $$$${n}\:\mathrm{knows}\:\mathrm{1}\:\mathrm{2} \\ $$$$\mathrm{everyone}\:\mathrm{knows}\:\mathrm{2}\:\mathrm{persons}\:\mathrm{and}\:\mathrm{noone}\:\mathrm{knows} \\ $$$$\mathrm{everyone}. \\ $$$$\mathrm{Did}\:\mathrm{i}\:\mathrm{misunderstand}\:\mathrm{the}\:\mathrm{question}? \\ $$
Commented by nburiburu last updated on 28/Jun/16
$${Be}\:{careful}: \\ $$$${if}\:\mathrm{2}\:{knows}\:\mathrm{3}\:\mathrm{4}\:{and}\:\mathrm{1}\:{knows}\:\mathrm{2}\:\mathrm{3}\:{then} \\ $$$$\mathrm{2}\:{also}\:{knows}\:\mathrm{1}.\: \\ $$$${So}\:{the}\:{relationship}\:{is}\:\:{in}\:{two}\:{ways}. \\ $$$${Also},\:{if}\:{you}\:{select}\:{any}\:{subgroup}\:{of} \\ $$$${two}\:{persons}\:{you}\:{should}\:{have}\:{to}\:{see}\:\:{in} \\ $$$${each}\:{person}\:\mathrm{2}\:\:{relations}\:{external}\:{to} \\ $$$${the}\:{subgroup}\:{made}. \\ $$
Commented by prakash jain last updated on 28/Jun/16
$$\mathrm{Thanks}.\:\mathrm{I}\:\mathrm{understand}\:\mathrm{the}\:\mathrm{question}\:\mathrm{now}. \\ $$