Monday, February 7, 2011

The Thanksgiving Hat Puzzle

You are hosting a Secret Santa, and everybody shows up for the drawing except one person. What if everybody wants to maintain the surprise? Your guests want no idea who their Santa is and no idea who anybody has. They want it purely, completely a surprise, also meaning no idea if somebody has better odds of getting a certain person. So that's it! how would you do that???
  • You only have pen/pencil, scrap paper, and hat! (no computer, phone, etc.)
  • Nobody else is around to help!
  • Everything must be random!
  • no time limit or anything like that

For an example on how my family's wasn't random(click full post for background story), I was the 3rd person to draw from my Nana's hat. I drew my own name, so I had to pick another and toss my name back. At that point, I knew that the two people who drew before me could not have picked my name. Bad. Also, Carolyn peeked to make sure Bob (who was absent) did not pick himself. So she knew his person. Bad.

Actually you don't need those materials exactly. You could put the pieces of paper in something like Easter eggs if that would make you more certain there is no way to tell. As long as it stays random and use simple/common items.

Click "See The Rest" for my solution.

The background story:

My family has relatively new tradition of doing a Secret Santa for Christmas. After a hefty Thanksgiving dessert, my grandmother (more affectionately, Nana Ann) brings an upside down hat into the dining room. Even after a few years this still confuses me when I first see it. "What the f*** Nana doing?" Turns out it is that silly hat full of names for the Secret Santa drawing.

This past Thanksgiving, Bob (my uncle) left either before or shortly after dessert. He wasn't there for the drawing. So Carolyn, my aunt, made sure Bob did not pick himself. Then we went around the table drawing names, throwing it back into the hat if we picked our own name. For such a simple task, it takes us a rather inordinate amount of time. Minutes later, most of us know who has who; for some reason my brother doesn't really like to keep his Santa a secret, my mother has a horrible poker face, and Christopher (cousin) couldn't care much less. Nana and I manage to stay mum.

I had this annoyed kind of feeling. But not because my family disclosed their Santas. For a moment, I knew how someone with long fingernails felt scratching a chalkboard, how an obsessive-compulsive felt stepping on a sidewalk crack. Our method of drawing … was not random! Grr!

If you found a solution to that, now try it with TWO people missing from the drawing. Once again, each person should have the same probability of drawing any other name with simple stuff like scratch paper, a pen/pencil, and a hat.

The solutions are in between the following horizontal bars in white text. Highlight for the answer.

It's pretty simple. Make name slips for everybody except for the absent guest. Randomly select a slip from the hat, and set it aside. Now, add a slip with that person's name into the hat. Once everybody has selected a name, if nobody has their own name, perfect. But if somebody did draw themselves, just start back from the VERY BEGINNING starting with the absent guest again.

With two guests missing it's a little more complicated. I'm using Easter eggs to make it easier to understand, but you could pull it off without them as long as everybody knows what they're doing. First, I would draw for "Sally" (the first absent guest) by putting everyone's name in a bunch of eggs except for her. The second guest, "Jason," now has Sally's egg placed in the hat. But now we do something different. This could be done as a solution to the first problem, but now we HAVE to do it this way with two missing guests. Now we know that Jason could potentially pick himself, because Jason's egg was in Sally's drawing. There's no way to avoid it; Jason could draw his own name. We need to do something that would let us know if Jason picked his own name, but otherwise not provide any information. So take something small and light (such as a cotton ball, or another slip of paper) and make sure form the beginning that Jason's egg has that object in it. After you draw an egg for Jason, check to see if it has the cotton ball in it. If it does, that means Jason drew his own name and we must start over. If it doesn't, we only know that it isn't Jason's egg (the slip with the name is still folded up inside the egg) and the show goes on. Once again, if somebody draws their own egg, start over from the very beginning.

If you still don't feel challenged, try comping up with a way for doing it with 3+ absent guests. I'm pretty sure there isn't a way to do that though. I could be wrong.

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