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Below are ##6## riddles. Everybody completing a riddle has a chance on winning the book "Dark Matter and the Dinosaurs".

Rules:

Thank you! I hope everybody will like these questions! Please provide any feedback you wish!

Rules:

- For an answer to count, the complete reasoning must be given, not just the answer.
- Do not answer a question you already know the answer to.
- If a question is already solved, you can still obtain recognition by generalizing the question!

- SOLVED BY mfb I have two buckets, one which can contain ##p## liters of water, and one which can contain ##q## liters of water. Both ##p## and ##q## are integers. You have access to a river with unlimited amount of water. You are asked to give the King ##n## liter water. You have no other buckets. For which ##n## is this possible? Detail the steps I need to take to complete this.

- SOLVED BY mfb In the euro system, you have coins of ##1## cent, ##2## cents, ##5## cents, ##10## cents, ##20## cents, ##50## cents, ##1## euro (= ##100## cents) and ##2## euro. I am asked to pay ##5## euros. In how many different ways can I do this?

- SOLVED BY RUber, Orodruin, PeroK, votingmachine I am the leader of a sect with ##1000## people (including me). I have recently declared that the entire sect should commit suicide. The entire sect stands in a circle. I point out somebody who is to commit suicide. After this we move clockwise and every second remaining person commits suicide. At which place should the leader stand in order to survive the suicide and obtain all the riches from the members? For example, if there were only ##5## members named ##1##, ##2##, ##3##, ##4##, ##5## and I say that ##3## kills himself first, then ##5## will go, then ##2## and finally ##1##. The leader should be at place ##4##.

- SOLVED BY votingmachine I have ##5## piles of ##1000## coins. There are two players. Player ##1## begins and chooses a coin. That coin is then removed and all the coins above it are removed too. Player ##2## does the same. Etc. The player who removes the last coin wins (as the other player cannot remove any coin). Do you wish to go first or second?

- SOLVED BY fresh_42, PeroK Two players start from ##0## and alternatively adds ##1## to ##10## to the sum. The first who reaches ##100## wins. Do you want to go first?

- SOLVED BY Zarqon, martinbn Dividing a cake fairly between two people is easy: let one person cut the cake in two pieces, let the other choose one of the pieces. How would you divide a cake fairly between three people?

Thank you! I hope everybody will like these questions! Please provide any feedback you wish!

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