Answer: Tuesday Teaser #8
Let’s work through this one logically, but before that let’s give some random names to our party guests to make it all a little easier. Suppose the guests are:
Adam || Angela
Bruno || Beatrice
Chris (me!) || Chloe
Darren || Danielle
Ewan || Emma
Given the three observations, nobody can possibly shake more than 8 hands (everyone except themselves and their guest). Now there are nine guests apart from me and they all tell me they shook a different number of hands. This means somebody must have shook each number from 0 to 8 guests’ hands.
In particular, we have one guest, Adam say, who shook all eight possible other hands. Hence everybody other than Angela shakes at least one hand. And therefore Angela must be the guest who shook nobody else’s hand.
We continue the same way: Now one of the remaining guests, Bruno say, must have shaken seven hands, that is to say all guests other than Angela and Beatrice. And hence Beatrice must shake only one hand as everybody else has now shaken at least two hands.
Similarly, we find that Darren, say, shakes six hands and Danielle shakes two, and that Ewan, say shakes five hands and Emma shakes three. Adding all this up leaves the answer - that both myself and Chloe shook four hands at the party.
