Gift exchange

Bitkidoku proposes this holiday nut. Six friends want to exchange gifts. Each person will buy one gift. To determine who they will give their gift to, they each put their name in a hat and take turns drawing. If a person draws their own name, they put it back and draw again. If the last person draws their own name, they all start over from the beginning.

How many possible outcomes are there?

Four-way word set

The Puzzle Podcast introduced (in episodes 5 and 6) a puzzle called, unaccountably, "GO Mental." Four words are given; three of them follow an unstated rule and one does not. For example:

twin triplet king queen

Which one doesn't fit? The puzzles provide a few seconds of wonderment and a pleasant little flash of recognition.

It occured to me that a good challenge would be to come up with a quartet of words based on four rules, such that each word obeys three rules and violates one. After a year, I came up with this set:

charger colt dolphin mustang

Instead of stating the rules, the solver is encouraged to provide a word that satisfies all four rules. And then to come up with a new quartet in under a year.

Ball drop protocol

Someone told about this phone interview question.

If you drop a ball from a high enough floor of a 100-story building, it will break into pieces when it hits the ground. You have two balls to test with. How do you determine the lowest floor that is high enough to break a ball with the fewest number of drops?

Bent coin flip

You and a friend want to make a decision by coin toss, but all you have is a beat-up old ducat, which you fear is slightly biased. How do you make the fairest decision in a reasonable amount of time?

Bernoulli coin flip

Nicolaus [Bernoulli] proposes a game to be played between Peter and Paul, in which Peter tosses a coin and continues to toss it until it comes up heads. Peter will pay Paul one ducat if heads comes up on the first toss, two ducats if heads comes up on the second toss, four ducats on the third, and so on. With each additional throw the number of ducats Peter must pay Paul is doubled. How much shoud someone pay Paul -- who stands to rake in a sizable sum of money -- for the privilege of taking his place in this game?
--Against the Gods

Il problema dei punti

Una brigata gioca a palla a 60 el giuoco e 10 p caccia. E fano posta duc 10. Acade p certi acideti che non possano fornire, e l’una pte a 50 e l’altra 20. Se dimanda che tocca p parte de la posta.
--Luca Pacioli, Summa de arithmetica, geometria, proportioni et proportionalita, 1494

A group plays a ballgame to 60 and each goal is 10. They stake 10 ducats in all. It happens by certain accidents they are not able to finish; and one party has 50 and the other 20. What portion of the stake is due to each party?