IIT JEE , AIEEE Forum - Mathematics , Algebra

laksy

Everyman who has lived on earth has made certain no. of handshakes prove tat no. of men who made odd no. of handshake is even

sboosy

Odd number of handshakes
Consider a situation where a man shakes hands with one other person only
now since in each handshake two persons have to be involved
(for every odd number of handshake of every one who shakes his hand) there r 2 persons involved
in all the total is going to be a multiple of 2 which makes it even
similarly for 3 handshakes
it is going to b same as above + 2 extra handshakes for every person
the 2 extra will give rise a even number for every person
so again the total will be even +even = even
thus for 5 it is (3(even number of shakes+ another 2 extra))
....
thus no of men who made odd number of handshakes is always even

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