We decided to do secret Santa in our office. And this brought up a whole heap of problems that nobody could think of solutions for - bear with me here.. this is an important problem.
We have 4 people in our office - each with a partner that will be at our Christmas meal.
Steve, Christine, Mark, Mary, Ken, Ann, Paul(me), Vicki
Nobody can know who is buying a present for anybody else. But we each want to know who we are buying our present for before going to the Christmas party. And we don't want to be buying presents for our partners. Partners are not in the office.
Obvious solution is to put all the names in the hat - go around the office and draw two cards.
And yes - sure enough I drew myself and Mark drew his partner. (we swapped)
With that information I could work out that Steve had a 1/3 chance of having Vicki(he didn't have himself or Christine - nor the two cards I had acquired Ann or Mary) and I knew that Mark was buying my present. Unacceptable result.
Ken asked the question: "What are the chances that we will pick ourselves or our partner?"
So I had a stab at working that out.
First card drawn -> 2/8 Second card drawn -> 12/56
Adding them together makes 28/56 i.e. 1/2.
i.e. This method won't ever work... half chances of drawing somebody you know means we'll be drawing all year before we get a solution that works.
My first thought was that we attach two cards to our backs... put on blindfolds and stumble around in the dark grabbing the first cards we came across... However this is a little unpractical and I'm pretty certain we'd end up knowing who grabbed what anyway.
Does anybody have a solution for distributing cards that results in our desired outcome?
I'd prefer a solution without a third party..