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Eight-people-are-seated-around-a-circular-table-Each-person-must-shake-everyone-s-hand-but-they-must-not-shake-hands-with-the-two-persons-seated-at-their-sides-How-many-handshakes-occur-




Question Number 911 by 112358 last updated on 22/Apr/15
Eight people are seated around  a circular table. Each person  must shake everyone′s hand but  they must not shake hands with  the two persons seated at their sides.  How many handshakes occur?
Eightpeopleareseatedaroundacirculartable.Eachpersonmustshakeeveryoneshandbuttheymustnotshakehandswiththetwopersonsseatedattheirsides.Howmanyhandshakesoccur?
Answered by prakash jain last updated on 22/Apr/15
This will same as number of diagonals in  an octagon.  ((8×5)/2)=20
Thiswillsameasnumberofdiagonalsinanoctagon.8×52=20
Commented by 112358 last updated on 23/Apr/15
Would it be possible to generalise  this problem where there are n   people and m number of persons  seated on both sides of each   person with whom hands cannot  be shaken?
Woulditbepossibletogeneralisethisproblemwheretherearenpeopleandmnumberofpersonsseatedonbothsidesofeachpersonwithwhomhandscannotbeshaken?
Commented by prakash jain last updated on 23/Apr/15
((n×(n−2m−1))/2)  2m, m people on either side  1, self  So each point is connected with n−(2m+1)  points.  Divide by 2 for counting each line twice.
n×(n2m1)22m,mpeopleoneitherside1,selfSoeachpointisconnectedwithn(2m+1)points.Divideby2forcountingeachlinetwice.

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