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## Main Question or Discussion Point

*Inspired by micromass' statistics challenge, I hope you enjoy it!*

Recently your financial situation has been less than optimal, and you are left with no other choice but to beg for money in the square in front of the king's palace. However, begging is strictly forbidden in that particular square, and, unfortunately, you are caught. The usual punishment is 20 lashes, but the king gives you a grace. He gives you the option to be let go unharmed, or solve a puzzle, with a reward, but also a punishment if you don't manage to solve it. Intrigued, you chose to accept it.

__The king will hide 5 identical diamond and 5 identical amethyst rings in 10 boxes. Both types are precious, but diamond rings worth more than amethyst ones. Your task is to guess which box contains which type of ring.__

**The King's Puzzle:**__Once you make a guess, you don't see if you guessed right or wrong, you have to move on to the next box.__If you guess either 0, 5 or 10 rings right, you will be sold as a slave (which is unfortunate). If, however, you guess exactly 8 rings right, since the king's birthday is on the 8th of August, you will be gifted all of the rings that you guessed right. If you guess any other number of rings right, you won't be awarded anything, but you won't be punished either.

Is there something that you can do to maximize your chances of getting mostly diamond rings (I forgot to mention that you're so greedy, amethyst rings just aren't good enough), or even any rings at all, but also minimize the chances of you being sold as a slave? Justify your answer.

__Say now that the king retains this 0-5-10 = punishment, 8 = reward rule, but changes the number of rings? For example, what if he gives you instead 10 diamond and 10 amethyst rings to guess? Can you generalize the rule?__

**Optional challenge 1:**__Are there numbers of rings to guess would you chose not to waste your precious time (which you could spend wandering around with no purpose) with, if the punishment-reward rule remains unchanged? Is there a number of rings that would maximize your chances of getting precisely 8 rings right?__

**Optional challenge 2:**Happy solving! If you enjoyed this puzzle, I will try to come up with a "sequel", and also try not to jump the shark with it, like so many movies these days

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