Seven students go on vacations. They decide that each willsend a postcard to thr

Question

Seven students go on vacations. They decide that each willsend a postcard to three of the others. Is it possible that everystudent receives postcards from precisely the three to whom he sentpostcards? **PLASE SHOW ALL YOUR EXPLANATION Seven students go on vacations. They decide that each willsend a postcard to three of the others. Is it possible that everystudent receives postcards from precisely the three to whom he sentpostcards? **PLASE SHOW ALL YOUR EXPLANATION

Explanation / Answer

NO it is not possible Sender  Recivers                               Recivers from 1-->2,3,4   2-->1,5,6 (has to send to 1) 3-->1,4,7 (has to send to 1) 4-->1,3,5 (has to send to 1,3) 5-->2,4,6 (has to send to 2,4) 6-->2,5,7 (has to send to 2,5) 7-->3,6, X (has to send to 3,6, X ie 1) if you consider each sender to be a node, and inbetween two nodesis one vector then this results in 10.5 vectors.This means that atone node will be short another and so it cannot make a completevector. since the vector represents 2 postcards, one person will send out 3and only recieve 2.

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