Originally posted by iamatiger
she shakes 4 people's hands.
In case of any demands for an explanation:
There are 9 people who have to shake different numbers of hands (Mr. Jones' handshakes are irrelevant). The maximum number of hands that anyone can shake is 8 and the minimum is 0. Therefore every possible different number of handshakes must be used.
Consider the person who shakes 8 hands, that puts every person apart from his spouse on at least 1 handshake, therefore his spouse must be the one who shakes 0 hands.
Now consider the 7 hand shaker, he will put every person, apart from HIS spouse on 2 handshakes, therefore his spouse must be the 1 hand shaker.
Likewise the 6 hand shaker partners the 2 hand shaker and the 5 hand shaker partners the 3 hand shaker.
As Mrs Jones' spouse is not counted she must be the 4 hand shaker, she puts her spouse on 4 handshakes so Mr Jones himself also must shake exactly 4 hands.