Yoruichi-san

When I woke up, my brain started working again... Is it just me, or do you start to see 8-dimensional vector spaces in everything when you're sleepy? *whistling*

Yep, I think that is the solution, its the one I got, too. Like I said, I didn't create this problem, and I don't know that much about computers. But I think the point was that additions take, like, nearly an order of magnitude less than multiplication. As for polar coordinates...this problem was actually suppose to be simple ;P.

Excellent. Btw, that chinese character in the picture is actually my last name (or first in chinese) ;P As for the Witch of Secrets' scroll...well, I'm kinda stuck. Bed for me, someone else figure it out. XP

Yoruichi-san's solution is elegant, but I want to sell concessions at that median divider, maybe set up a traffic island, possibly a theme park. Lol...what they didn't tell you was that these four towns are all towns of super-genius scientists (like Eureka ;P), and they've all established teleporters to each other's towns already, and this whole exercise is a diversion to keep the board occupied so they don't have to try to explain the safety procedures of teleportation to a bunch of non-scientists. Tony Stark to Bruce Banner in The Avengers, discussing gamma radiation: "Finally, someone who speaks English!"

Minor details about the fish lines An excellent strategy! Although, in the story, I was trying to convey (and I guess didn't) that they didn't have a lot of time to come up with a strategy of say "you raise your hand when to indicate a particular arrangement". But major points to Bushindo for his solution. Also, I was trying to convey (by the rules) that they couldn't speak or look at each other until their respective gong rang, so there needed to be another element to alert them to the others raising their hands, hence the fishing line, which Bushindo correctly arranged. Looking at the final shape...well, it's befitting the most benevolent king, don't you think? Anyways, let me ask this question then. If there was no time to devise and agree on a strategy, hence allowing the fishermen only to raise their hand when they knew their own color of hat, what is the algorithm for the first fisherman?

Nice try, but writing 22,6 as 226 would definitely make the MathGirl inside of me angry, and you wouldn't like MathGirl when she's angry. ;P "MathGirl, 96!"

That's the other part of the puzzle . Plasmid was very close, the answer to that part just needs to be refined to fit the specified rules laid down by his oh-so-munificent majesty. ;P

Thanks, rookie! Bonanova: lol, clever. Yeah, division pretty much counts as multiplication (of the inverse), and subtraction counts as addition (of the negative)

I couldn't resist responding to happy chance...;P Not my own creation, but you don't need to know too about complex numbers to solve it, just the basic definition of i =sqrt(-1) should suffice. So the straightforward method of computing the product (a+bi)(c+di) = (ac-bd)+i(bc+ad) requires four (real) multiplications and two additions. However, most computers require a significantly more time to compute multiplication than addition. Find an algorithm for computing (a+bi)(c+di) with only three multiplications.

I think you're right

I think I see where there may be some confusion. Let me clarify for those unfamiliar with my style: the two questions in the OP are separate, hence they are set in different paragraphs. The second question is not [specifically in the arrangement of the first question], but, in general, in any arrangement, how will the first fisherman figure out what color his hat is? I'm asking for an algorithm/set of rules that he should follow.

Good work, but not quite finished. To complete it, consider all possibilities, not just the most convenient ones. Alternatively, let's ask: What is the non-zero minimum number of fisherman who can raise their hand after the 2nd gong but before the 3rd gong? That is, if any raise their hands at all, what is the minimum? You're definitely on the right string , but remember, they aren't allowed to move except to turn their heads in the specified directions to look, or to raise their hands to declare they know their color. And yes, of course, it would have been easier to make the rules, and be effectively equivalent, if the positions of 2's and 3's were switched...but the king likes the feng-shui of this orientation, and, well, he is the king. ;P

Something like this, in a very big room, where 1 gets to look at the two 3's after the first gong (he starts facing outward but is allowed to turn to both sides slightly), the 2's get to turn to look at each other and then turn to 1 after the 2nd gong (closing their eyes in between, and directed by the king and his guards), and the 3's get to look at each other after the 3rd gong, and there is no cheating (or else there be mass beheadings). There may be another element to the circle...but that's kinda part of the puzzle ;P.

Having grown ennuied of torturing prisoners on death row with hat problems (after all, where was the suspense if they had nothing to lose?), the sadistic king decided it was time to expand his horizons. As luck would have it, today was the day the fishermen's guild was sending its tribute, brought by five of its most capable members. After graciously receiving a crate of fresh, lovely salmon, mahi mahi, and white tuna, the king thanked his guests by promptly ordering their arrest. "But what did we do?" the unfortunate artisans asked. "You are harming the kingdom. Your practices are not..." the king searched for the politically correct buzzword of the day, "...sustainable. Hence, you will be put to death." The fishermen pleaded and begged for mercy. The king reclined in his throne, covering his smile with his generously ringed hand, and savored the moment. Finally, he raised the hand for silence. "I am a benevolent and fair ruler," he proclaimed, "Hence, I will allow you one chance to save yourselves." He gestured to his manservant, who, all too familiar with the drill by now, went to fetch his box of hats. The king continued, "After my manservant returns, I will have you all stand, facing the directions I specify, with eyes closed, in a circle in front of me." He gestured towards the expansive floor of the throne room. "Then I will have my manservant place a hat on each of your heads. There are three white hats and two black hats. Without speaking or moving in any way other than I direct, you must determine what color the hat on top of your own head is, and when you do, you may raise your hand and my manservant will come to you and you may whisper the color in his ear." "So if one of us figures out the color of out hat, we all go free?" asked one fisherman who had heard mention of the king's tyrannical games before. But the king shook his head in a lordly manner. "You must ALL determine the color of the hat you each wear. If one man declares an incorrect color, you will all be executed." "But, surely, you can't expect us to figure out the color of our hat with no information...your majesty," another fisherman protested. "Of course not," the king stated. "I am much too beneficient." He nodded towards a large bronze gong residing in one corner. "When the gong sounds the first time, the man closest to me may look at the hats of the two standing closest to him. When the gong sounds the second time, the two men farthest from me may look at each other's hats, and the hat of the man standing closest to me. When the gong sounds the third and final time, the remaining two men may look at each other's hats. My guards will be stationed closely to prevent cheating. If cheating is attempted, you will all be executed." The fisherman shot glances at each other. "But, your munificent majesty," one finally spoke, "we need something more, if we are not allowed to speak or move other than to look or raise our hands." "Well, too bad," the king replied, yawning. "That's all I'm giving you." The most diminutive and bravest of the fishermen asked, "What if we use something we already have? Then you don't have to give us anything." The king stroked his chin. The only thing the men had on them, besides their clothes, was fishing line. He shrugged. "Sure, let's just get this party started." The fisherman huddled together for a few moments, then positioned themselves as directed, evenly spaced in a large circle. Shortly, the manservant returned with the hats and the game was afoot. What is the maximum number of the fisherman that can raise their hand after the second gong but before the third gong? How will the fisherman standing closest to the king determine what color his hat is?

Nice! I just realized I made an error with the original for #17 (it's suppose to be 133), so I'm glad you provided me with an excellent alternative . Sorry! #6 is obviously not the original, but is acceptable (in terms of fitting the puzzle, at least @_@) Your answer to 12 is very good and very close to the original, which is more of a self-descriptor for me. I know these are probably really hard, so I may drop a few more hints from time to time. Such as how there may be something fantastic about 2 and 13 ;P.

Oh, so close... But I think most of them require a trick - see Thalia's answer for 9: Spot on for #9 . The others are really good answers, but not the original answer. And it brings up some good points about the "rules" I set for myself: Hence, where a normal rebus would have like TISTITCHME as "a stitch in time", with numbers I need some indication of one number inside another number, such as parenthesis *cough*. I tried to demonstrate that with my hint which in itself was somewhat riddle-esque. At home with my family, I speak chinglish, here I guess I speak...uh...engriddle? C'est parfait. Good to hear from you again 39-san ;P ® Good to see you too, professor. Lol, maybe you should make the sequel to this thread, then ;P (and I thought it was TM?)

Great answers from everyone, I love your creativity. But the number is very specific to each one, not the number's properties (even,odd, prime, etc) Molly Mae is on the Scent ;P Further hint is in my sig. Good luck!

Technically, the title of this thread was originally "I know I spend too much time on Brainden when..." -When I come back after a long hiatus and reread this thread. Ahh...good times. ;P

It doesn't really matter.

Interesting line of thought, but that's not what the numbers mean ;P.

This. Is. Awesome. The tone is phenomenal, even better than the CRY anime I've seen. I look forward to the next chapters. And I hope that there's a second season of Umineko that explains wth was going on as well as the second season of Higarashi did. I absolutely love the concept of a puzzle/adventure/story. So much I'm inspired by it. Hmm...