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

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