At a certain convention participate 100
persons. It is known that each participant personally knows (and is known by) at least 67 others.
A certain lady would like to dine with other 3 at the same table, provided they know her and they know each other.
Prove that this is possible.
Advise how actually she can arrange it.
Let us call the lady A. From the list of 100 names ERASE all those that don't know her- i.e. 32 names- she knows herself for sure...and you are left with 68. invite any participant on the list and erase another 32 that know neither A nor B.
Does anyone care to complete my explanation to cater to A's initial whims?