Showing posts with label blindfold. Show all posts
Sunday, August 16, 2015
Boxes, Beads, and a Blindfold
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You have been named as a traitor by the King, the punishment for this
crime is death. Although he is a cruel tyrant he gives you one last
chance at freedom. When you are finally brought before him he has this
to say to you:
"There are 100 beads, 50 black and 50 white. You will be allowed to draw one bead, whilst blindfolded of course. If it is black you will be condemned to death, if it is white you will be set free".
So far so good you think to yourself, at least I have a 50/50 chance.
"The beads will be distributed amongst four boxes by me," he continued. "You must select a box by opening it, draw one bead from it and then present the bead to the court. Thus will your fate be decided".
Upon saying this a cruel smile appears on the King's face and you suddenly break into a cold sweat as you remember that the King is both very wicked and devilishly cunning.
Assuming that the King is incredibly smart, evil, thinks that you are a stupid, uneducated peasant and wants to minimise your chance of freedom, what strategy should you employ, and what is the probability of surviving?
"There are 100 beads, 50 black and 50 white. You will be allowed to draw one bead, whilst blindfolded of course. If it is black you will be condemned to death, if it is white you will be set free".
So far so good you think to yourself, at least I have a 50/50 chance.
"The beads will be distributed amongst four boxes by me," he continued. "You must select a box by opening it, draw one bead from it and then present the bead to the court. Thus will your fate be decided".
Upon saying this a cruel smile appears on the King's face and you suddenly break into a cold sweat as you remember that the King is both very wicked and devilishly cunning.
Assuming that the King is incredibly smart, evil, thinks that you are a stupid, uneducated peasant and wants to minimise your chance of freedom, what strategy should you employ, and what is the probability of surviving?
Notes:
- The King whilst evil won't cheat.
- The trick is to work out how he plans on distributing the beads to minimise your chance of success.
- As soon as you stick your hand in one of the boxes you must draw a bead from it.
- The boxes and beads light and portable, however you are not allowed to remove them from the area.
- The King thinks you are stupid.
Boxes, Beads, and a Blindfold Puzzle Solution
The king puts 1 black bead in 3 of the 4 boxes and all the other beads (both black and white) in the fourth box.In the kings' view, you will just randomly pick a box because you are so stupid. This gives you barely 1 chance out of 8 to pick a white bead (1/4 to pick that one box containing white beads multiplied with almost 1/2 to pick a white bead out that box).
Assuming each of the four boxes are identical, by picking up each box in turn, you will be able to tell by weight or the rattling noises which one of the boxes contains the mixed beads. Picking the box with the mixed beads will mean that you have a slightly better than 50% chance of living.
Thanks to "Ben Leil" and "Kobold" for posting solutions in the forum
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