The handshakes.
Maya is Shyam's wife. Maya and shyam have hosted a dinner party and they have invited three more couples. At the beginning of the party , some handshakes occur. Now , a husband will not shakes his own wifes hand and vice versa . Just before dinner, Shyam asks everyone to state the number of handshakes they have done. Everyone answers with different numbers. No two people have done the same number of handshakes. Then, how many handshakes has Maya done?
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1 solution
Now , since a husband cannot shake his wifes hand and vice versa, 1 person can have a maximum of 6 handshakes. Then the only possible answers wr can get are: 6,5,4,3,2,1,0. Shyam has asked 7 other people to state the munber of handshakes, hence these are the answers he received. Since there is no other possible number, Shyam must have done the same number of handshakes as one of them.
Now, lets imagine a couple A. The wife has done 6 handshakes . That means that she has shaken hands with everyone other possible(excluding herself and her husband). This means that everyone else must have done a minimum of 1 handshake. But since the answers must have 6,5,4,3,3,1,0 the only person who can have done 0 hanshakes will be her husband . That means that the people who have done 6 and 0 handshakes are a pair. By the same logic the ones with 5 and 1 , 4 and 2, 3 and 3 will be couples. Since shyam has heard different answers and must have had the same number of handshakes as one of them, he must have done 3 handshakes, since 3 is rhe only repeated number. Since 3, 3 is a couple, Maya must have had 3 handshakes.