Great Galileo"s Ghost
Cranks have always loved to compare themselves to Galileo. Sick of this, one day Greta Christina decided to set them straight once and for all. To do this, she decided to go on a fictional journey to the afterlife to find Galileo himself so he could explain to them why they"re acting like idiots. However, when she reached the afterlife, she ran into a little problem.
It seems that one day, Galileo accidentally touched a noodly appendage he shouldn"t have, and ended up with a couple clones. On top of this, the three are cursed to always stay together and that if any yes-or-no question is posed to one of the three, they all must answer it. Any other type of question will be ignored by all three. Each of the clones plus the original has a specific curse on them, but it"s unknown who has which curse. One of the curses requires the bearer to tell the truth to any question, another curse requires the bearer to lie in response to any question. The third curse causes the bearer to randomly choose between telling the truth and lying before answering each question.
Each of the Galileos knows whether it"s the original or a clone, but without knowing which bears which curse, it would be tricky to figure it out. Is there a questioning procedure that would work here?
Now, Greta can"t go back to the real world with three mixed-up possible Galileos, but fortunately, there"s a way to break the curses. If any of them is ever faced with a question they can"t answer (for instance, they"re bound to tell the truth for this question, but the question has no truthful answer that doesn"t result in a paradox), they"ll go "Voip!" and vanish (so sayeth the FSM). If the two clones both vanish, the original Galileo will be freed from all the curses on him. However, he could vanish too if he"s asked a question he can"t answer, and if he does, it"s game over. Is there a way to target out the two clones and make them vanish while keeping Galileo safe?
If you can accomplish that, one further challenge: Can you make both clones vanish with a single question, even if you haven"t previously figured out which one is the real Galileo?
Super-Scammer Secrets
Lord Runolfr recently got a couple of e-mails from scammers, raising my suspicions that something big was afoot behind the scenes. I called up a few contacts, did some research, hired a few James Bond-alikes, and here"s what I"ve figured out:
There"s some evil mastermind behind the whole plan, and he"s about as supervillanous as they come. This of course means that he wants to capture one of my James Bond-alikes and subject him to an intricately detailed explanation of his evil plan before killing him in a creative way. Apparently, the way he"s decided to go about this revelation is through an overhead transparencies with the key points of his evil plan (you"d think he"d have better technology than my high school, but he"s out to make money, so he saves it where he can).
Now of course, he"s wary of this transparency falling into the wrong hands, so he"s come up with a plan to keep things safe. He"s figured out some method to spread the information across multiple sheets, arranging it so that if we get a hold of any two, we"ll still have no idea what he"s planning. So, what we need to figure out now is some possible ways he might have done this, so if we manage to get our hands on more than two, we"ll know how to read them (if it"s not immediately obvious). What are some possible things he could do? Remember that he"s out to save money, so splitting it up to have a single word on each slide or something huge like that doesn"t seem too likely.
Harebrained Hat Help
Orac reports that the University of Maryland"s Shock Trauma center has gone to the dark side, citing how Reiki therapy is now being used to "help" patients. Well, I did some digging of my own, and it turns out this isn"t the craziest thing they"re doing. They"ve got something even dumber going on, called "Colored Hat Therapy." Here"s how it works:
A bunch of patients are seated in a circle, and a hat is placed on each one"s head. They don"t know the color of their own hat, but they can see everyone else"s hat. There are many colors of hats, but each color present shows up on at least two hats. The patients sit in the room for a while, and every couple of minutes an announcement comes on the PA system, asking anyone who"s figured out the color of their own hat to announce it and then leave the room. The theory goes that the magical hat energy must have seeped into their brain, and they"re now cured.
Of course, most of the time it doesn"t work so well, and people guess incorrectly about their hat color, miss their chance to get it and never figure it out, or get screwed up by inferring wrong things from other people"s mistakes. However, one day, purely by chance, everyone brought into the room was an expert at logic puzzles, and they all managed to figure out the colors of their hats. How did they do this?
(Aside: When one of these experts left the room, a nurse noticed that the wound he was suffering from hadn"t magically healed, and this therapy was quickly abandoned.)
Singular Sword Slashes
Martin Rundkvist recently uncovered a unique 16th century sword, and he was wondering how many lives it might have taken. Well, I did a little
It turns out this sword was used in a ceremonial mass execution. 100 condemned prisoners were brought out and given one last chance at life. They were all stood up in a line and had a hat put on their head, colored either red or blue. No one knew the color of their own hat, but they could see the color of every hat in front of them. If they guessed correctly, they were spared, but if they guessed incorrectly, they were killed on the spot. This particular sword was used for the killings, and it was so fast and efficient that none of the prisoners in front would be able to hear a sound from the death, and so would have no idea if the guess was correct (though they would be able to hear the guess).
Unfortunately, I didn"t see the actual procedure, but I did learn two things that might give us a clue as to what happened: First, the prisoners were given a chance to discuss a plan amongst themselves before the ceremony and decide on it. However, the executioner was listening in and would likely set up the hats to thwart the plan as best as possible. The second thing I learned is that these prisoners were all condemned to death for being part of a "dangerous cult" - which was actually more along the lines of Mensa. So, these are pretty smart people, and we could trust them to come up with a pretty good plan.
Putting this all together, what probably happened during the ceremony, and how many lives did the sword take?
Ending Erroneous Expectations
The Sexy Secularist writes in about how he was able to persuade his mother against recommending the atrocious woo film What the (Bleep) Do We Know?. You see, personally, I know that the whole Law of Attraction thing is bull. Why? Because I was expecting at least one post sent in would have some tenuous connection to pirates and allow me to bring you this classic puzzle. But nope, no pirates. Well, screw you guys, I"m doing pirates anyways!
A crew of 5 logic pirates comes upon a treasure of 100 gold coins. According to the rules of the logic pirates, to distribute the loot the most senior pirate must first propose a plan, and then they"ll all vote on it. If at least half agree with the plan, they"ll go with it. If not, the most senior pirate has to walk the plank, and then the next most senior pirate has a chance to propose a plan. This continues until a plan is accepted.
Each pirate is perfectly logical and has the following priorities they will strictly pursue: First, they don"t want to die. Second, they want to get as much money as possible. If everything else is equal, they"d rather see more of their seniors walk the plank.
So, what plan can the most senior pirate of this group of 5 propose that will get him the most coins? Figured that out? Now, try the situation with 6 pirates and only one coin; what happens there?
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