unreality

use Euler's identity, which is the special case of Euler's formula, the equation for going around a circle with a real x axis and a nonreal y axis the special case is: epi*i + 1 = 0 which comes from this: epi*i = -1 which comes from this: etheta*i = cos(theta) + i*sin(theta)

no, at least not that's been found, I think. The number 27 takes like a lot of steps. Like over a hundred, I think. And, let's say you have 2^100. A huge number, I'm sure. But it only takes 100 steps to reach 1. So I think it jumps around Wait I found the list for 27, it takes 111 steps: 27, 82, 41, 124, 62, 31, 94, 47, 142, 71, 214, 107, 322, 161, 484, 242, 121, 364, 182, 91, 274, 137, 412, 206, 103, 310, 155, 466, 233, 700, 350, 175, 526, 263, 790, 395, 1186, 593, 1780, 890, 445, 1336, 668, 334, 167, 502, 251, 754, 377, 1132, 566, 283, 850, 425, 1276, 638, 319, 958, 479, 1438, 719, 2158, 1079, 3238, 1619, 4858, 2429, 7288, 3644, 1822, 911, 2734, 1367, 4102, 2051, 6154, 3077, 9232, 4616, 2308, 1154, 577, 1732, 866, 433, 1300, 650, 325, 976, 488, 244, 122, 61, 184, 92, 46, 23, 70, 35, 106, 53, 160, 80, 40, 20, 10, 5, 16, 8, 4, 2, 1 here's a graph of the numbers 2 to 9999 and their total stopping time: a fractal made from the sequences:

Yeah, it's about PROVING or DISPROVING that it will ALWAYS end in the sequence 4,2,1,4,2,1,4,2,1...(etc)

You mispelled some of those: Feramt should be Fermat Pythagaros should be Pythagoras Wiles should be Willes (I think) anyway, yeah. I would also like to be a coauthor ;D lol. I was thinking we could discuss it or something. I dunno. Somebody will be the first to solve it, if it's solvable which I hope it is

I agree ;D I think it's hard for theists to grasp the concept at first. They are stunned or something that we don't believe in a god and seem like they refuse to believe it at first. They ask things like "Wait- is the universe your God? Is science your God? Isn't atheism a religion too?" etc. Atheism isn't a religion- it's a lack of one. And like I said, in the post above octopuppy's, we truly appreciate the beauty of the world we live in

Probably many of you have heard of the infamous and unsolved 3x+1 problem. Many others have not, I'm sure. Here it is, in my words: ***** Take any integer greater than zero. Call this number x. If it is even, halve it. In other words, x becomes x/2 If it is odd, x becomes 3x+1 The sequence, for all numbers tested so far, ends up in the endlessly repeating loop of 4,2,1,4,2,1,4,2,1... While many numbers have been tested by computers, this doesn't prove or disprove the conjecture that the sequence will fall into this loop. Can you provide a counterexample (it would have to be BIG), or give a proof as to why it always iterates to 1, or a proof why it sometimes doesn't? Will you be the first? Just curious to see what you guys find.

I didnt find this problem until now I didnt look at any of the posts other than the top one so I hope there was no changes made that werent edited onto the OP anyway it has a 1% chance to switch your result if you are a drug-user or a non-drug user, in either case it has a 1% chance to misidentify Tom has a 99% chance of being innocent. When the test came up positive, that meant either: 1) he's a drug-user, and the test's 99% chance of accuracy worked, showing him as a drug user 2) he's innocent (99% chance overall) but the test misidentified him as a drug user, which it had a 1% chance to do so the chance that he's a drug user is 1% the chance that the test was correct is 99% the chance that he's NOT a drug user is 99% the chance that the test was inccorect is 1% clearly I dont need to do the math, each chance- innocent and drug-using, have equal numbers, just in different order. Therefore his chances of being a drug user is 1/2, and his chances of being innocent are 1/2

Wow! Good one! 5 stars ;D the fallacy is "the less you forget, the more you know" is not necessarily true. You could forget 50% of what you know, or you could forget 25% of what you know, either way you are knowing less, you are not knowing more just cuz you forgot less. Though it could be rewritten as "the more you retain", though it doesn't need a problem, it's not a paradox but a circle-of-life type thing. Awesome!

Since the debate has moved to this, I am happy to join in... Duh Puck said a child cannot do such evaluations, but when I was very young (i am younger than 20 now) I did figure out for myself that religious people were misguided, and wasting their time- because God doesn't exist. A theist might think that's a crushing conclusion, or they might think that it would sap the life out of life (if that makes sense), but they'd be wrong. I was happy when I realized that the universe was beautiful, and its own creation, not some guy with a white beard baking up some galaxies in His Divine Oven. Clearly it is natural to believe in higher powers, since humans have been doing it for centuries. The need to explain everything around us is strong. And, especially in earlier times, without the science and knowledge to explain things, it seemed that a god would be necessary. But it's not, and hence the world is beautiful... with a god it seems uptight, a network of people, all following rules. But without a god, it is chaotic and wondrous Anyway, I hope that if/when I have kids, they make an informed decision for themselves. Yes, I will be probably be biased toward atheism, but as Duh Puck and Scraff have said, that's a good thing, since I am firm in my own knowledge of that

Nice, bonanova. That's pretty sweet!

Yes, power corrupts. of course it does but saying absolute power absolutely corrupts and then saying that it wouldn't corrupt you is foolish. So you're special somehow? you basically said "Power absolutely corrupts everyone- except me of course." Explain why power wouldn't corrupt you, please, and I'll believe you

My dad = atheist, I think. We don't really talk about it, but kinda imply it I think My mom = stout Christian, as her family, of course. She would send me to all kinds of religious stuff when I was younger. I was too young to understand what the old guy in the silly white robes was saying, so I never really had a chance to be brainwashed or anything. I got to make a decision for myself. And I did, and it's only been strengthened since, seeing people in church monotonously reading and repeating the words appearing on the screen. Anyway, yeah. I made my own choice freely, and it was atheist, despite my mom's side of the family (definitely not because of it, I didnt become an atheist to be a rebel or something like that, or because they made me go to church, etc. They DIDNT make me go to church.) long story short, when you're left to truly make an unbiased decision, it's usually the best one.

Yep, and to brhan: there are number bases based off of irrational numbers, but they're kind of complicated lol. My favorite is phinary, just cuz the Golden Ratio (and fibonacci numbers) are so amazing anyway, how I would mathematically solve #3 if I didnt already know the answer: 10101 in base x is, in other words: x0 + x2 + x4 in base 10 or 1 + x2 + x4 in base 10 changing 273 from base x+6 into base 10 is also easy: 2*(x+6)log(100) + 7*(x+6)log(10) + 3*(x+6)log(1) or: 2*(x+6)2 + 7*(x+6)1 + 3 now that they are both in base 10, they can equal each other: 1 + x2 + x4 = 2*(x+6)2 + 7*(x+6)1 + 3 subtract 1 from both sides x2 + x4 = 2*(x+6)2 + 7*(x+6)1 + 2 (x+6)2 is (x+6)(x+6), which is x2+12x+36, all multiplied by 2 is 2x2+24x+72 7*(x+6)1 is 7x+42 x2 + x4 = 2x2+24x+72 + 7x + 42 + 2 now we have a ton of like terms on the right side to merge: x2 + x4 = 2x2 + 31x + 116 subtract x2 from both sides x4 = x2 + 31x + 116 subtract x4 0 = -x4 + x2 + 31x + 116 *-1 0 = x4 - x2 - 31x - 116 factor 0 = (x-4)(x3+4x2+12x+17) From there, what can easily turn that into 0. The clear answer is 4, cuz 4-4=0, which would negate the rest of it. If you try that, 10101 in base 4 is 273 in base 10 (4+6) I believe this was brhan's method. This is the mathematical/algebraic way to do it. The logic way to do it, which is probably what I would have really done, is: * x+6 cant be 7 or smaller, cuz a 7 appears in the number so it would carry over as a 10 if x+6 was 7 or lower. Therefore x+6 is 8 or more * which means x is 2 or more * x+6 could be more than 10, but no symbols were used in 273 so we're not sure if x+6>10 yet, though it's unlikely, since no symbols were used in 273, so it's not showing the part of the base, and what symbols would you use, letters..? To see if that's an option, figure out if x was higher than 4 and see if that's a possible solution. However if x was higher than 4, for example 5, than 1+5^2+5^4 = 651 in base 10, or, in base 11, 542, already much too big than 273 * so our range is x=2 or 3 or 4 * if x was 2, simple binary, then x^4+x^2+x^0 is 16+4+1 = 21 in base 10, which is (16=20)+5 = 25 in base 8 (8=x+6 if was x was 2). Clearly 25 is much less than 273. * I could try x=3, but I can already see that 1+9 is 10 in base 10, or 11 in base 9, so 3^4 would have to be 262 in base 9, but I know that 3^4 is 9^2 and 9^2 is 81 in base 10- which is very cleanly 100 in base 9. 100+11=111 in base 9, not 273. Not even close. So I dont even need to check base 3 fully * the only thing left is x=4 * 1+16+256 is 273. Yay! The number! But wait- dont you have to convert it to base 10, so it will change *sinking feeling* But not! Because if x is 4, than x+6 is 10. 273 is in both base 10 and base x+6. Therefore x=4

Ah you did it from the inside out. I see. For the 2d one I just quickly saw it was 2x+2y-4, though it's not as simple for the 3d one. I'll do what you suggested!

To brhan: yep you got it To eventhorizon's last post: Exactly there are no dumb questions (well sometimes there are lol) oh and I was wrong about my formula for shaded cubes. It's obviously not 2x+2y+2z-8 when you think about it for a second. It's all 6 faces, minus the shared strips so that's 2xy+2yz + 2xz - shared strips one sec on the shared strips ;D

You got #3 right ;D as for the 3d rectangular prism with border cubes shaded: 2x+2y+2z-8 = number of shaded cubes 2x+2y+2z-8 = xyz/2 *2 4x+4y+4z-16 = xyz +16-xyz 4x+4y+4z-xyz = 16 *-1 xyz-4x-4y-4z = -16 hmm. Not sure how to make that factorable lol. There's *probably* a way, I'll think on it

lol, by our definition, we don't believe in a Creator. Understand now? There are various theories as to the origin of the universe, such as the Bing Bang, string theory, etc. I don't know too much about those, though my personal inclination is that time/universe has been around forever, maybe the universe came from the Big Bang, which was condensed from the previous universe which wound itself back into a tight ball and exploded again, ie, repeating process. Though science has many theories, that's the point. I strongly recommend that everyone click on this link and read it. It has good arguements!

Statman, your #2 answer is correct, though for #1 you might be surprised to know there are only two answers (or 4 if you're picky). Look at my spoiler in the post above yours on the first page your answer is correct, but you only went halfway

Here's another riddle, I just thought this one up: 3. In base x, a number is 10101. The same number is 273 in base x+6 What is x? (ie, the base of the first number)

ah thanks, bonanova b^2 + c^2 = s1^2 + s2^2 + s3^2 + s4^2 458 = s1^2 + s2^2 + s3^2 + s4^2 so now what? How do you solve for the s's? There could be a zillion answers, right? Or do you somehow use s1+s2=s3+s4 to help narrow it down? I'm still confused ;D

EventHorizon, 0x0 wouldnt be a rectangle ;D it would be a single point. Like how 1x0 rectangle is actually a line. A 0x3x3 rectangular prism isnt actually a 3d rectangular prism as one of its dimensions is 0- it's a 2-dimensional object, as geometry goes. If a dimension is 0 then it's not counted as a dimension in geometry- it has to have some value to extend the axis in that direction. We don't say that a square has 5 dimensions if its 0x0x0x2x2, know what i mean?

"One of them is not the Lone Ranger" you said- the OTHER one is ;D haha like that problem where two coins total 30 cents, one of them is not a nickel. The OTHER coin is. lol.

Did the police find rugburns on the dead guy's body? Or "tire-burns"? Or maybe one of them was just more susceptible to the beating. Or the wheel popped, the spare tire had to be used, then later they bought a new matching tire and threw the spare tire back in the trunk- hitting the head of one of the guys, knocking him out but not showing signs of beating, so the other person freely used the spare tire for air on the rest of the journey (which is less cuz they had to open the trunk twice throughout the trip, so there would be enough air through those sections of time, and with opening the trunk twice, and then the spare tire, one person could easily make it while the other was passed out for the rest of the journey so the spare air wasnt being shared with him. He died. Hopefully the criminals that did this are in jail

bonanova is correct the "guy" wrote it in English, later getting the help of Jacques to translate it, and then leave a thank you message (and a thank you message for translating the thank you message, and then again, and so on... or not). Storm, the amount of paper doesn't matter- there's a logical solution as to why it's not an infinitely repeating line. The answers and my methods: