# More Handshaking

THUDandBLUNDER
Posers and Puzzles 16 Jun '04 14:24
1. 16 Jun '04 14:242 edits
Mr and Mrs Jones invite, four couples to a dinner party - the Whites, the Clarkes, the Greys, and the Browns. Some of the people have met before and some haven't. When they arrive All the people who haven't met before shake hands, and then Mr Smith asks each of the guests and his own wife how many hands they each shook. He receives a different answer from each person he asks. How many hands did Mrs Jones shake? (You may assume that everybody has met his own spouse before.)
2. 16 Jun '04 15:56
Originally posted by THUDandBLUNDER
Mr and Mrs Jones invite, four couples to a dinner party - the Whites, the Clarkes, the Greys, and the Browns. Some of the people have met before and some haven't. When they arrive All the people who haven't met before shake hands, and then Mr Smith asks each of the guests and his own wife how many hands they each shook. He receives a different answe ...[text shortened]... w many hands did Mrs Jones shake? (You may assume that everybody has met his own spouse before.)
How did Mr Smith get to ask the guests that when he wasn't at the party?
3. 16 Jun '04 16:01
Originally posted by iamatiger
How did Mr Smith get to ask the guests that when he wasn't at the party?
Good point.

But now I can't correct it.
What's with this annoying time limit for editing?

OK, here it is again:

Mr and Mrs Jones invite, four couples to a dinner party - the Whites, the Clarkes, the Greys, and the Browns. Some of the people have met before and some haven't. When they arrive all the people who haven't met before shake hands, and then Mr Jones asks each of the guests and his own wife how many hands they each shook. He receives a different answer from each person he asks. How many hands did Mrs Jones shake? (You may assume that everybody has met his own spouse before.)

.
4. 17 Jun '04 14:14
Originally posted by THUDandBLUNDER
Good point.

But now I can't correct it.
What's with this annoying time limit for editing?

OK, here it is again:

Mr and Mrs Jones invite, four couples to a dinner party - the Whites, the Clarkes, the Greys, and the Browns. Some of the people have met before and some haven't. When they arrive all the people who haven't met before shake h ...[text shortened]... y hands did Mrs Jones shake? (You may assume that everybody has met his own spouse before.)

.
she shakes 4 people's hands.
5. 17 Jun '04 18:012 edits
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.