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2 pointsIn our circles you may find A laugh, a wink, a grin But pressure us we'll likely snap And send away our kin. We don't do much, we go to pot Such simple ones are we But with your hand we take command Or from you we will flee.

2 pointsAgree. When I hit the send button, I realized my thinking was too simple. But instead of deleting my post (moderator privilege) I left it to take its licks.

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2 points(This puzzle is from a blog called By Way Of Contradiction.) Imagine you have a circular cake, that is frosted on the top. You cut a d degree slice out of it, and then put it back, but rotated so that it is upside down. Now, d degrees of the cake have frosting on the bottom, while 360 minus d degrees have frosting on the top. Rotate the cake d degrees, take the next slice, and put it upside down. Now, assuming the d is less than 180, 2d degrees of the cake will have frosting on the bottom. If d is 60 degrees, then after you repeat this procedure, flipping a single slice and rotating 6 times, all the frosting will be on the bottom. If you repeat the procedure 12 times, all of the frosting will be back on the top of the cake. For what values of d does the cake eventually get back to having all the frosting on the top?

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2 pointsI swear: 1) To strangle the next person who uses 'suicide' as a verb. 2) That if I offended or hurt you in any way, I didn't mean it. 3) That I'll stop procrastinating. Tomorrow. Add whatever you swear.

2 pointsPersonally, the original reason I believed in God is that an adult told me he existed when I was little and, being little, I took their word. But over time, I've listened to people talk about their experiences with God and seen it with others. I think I've seen Him get me through a lot of stuff the past few years that I don't think I'd have been able to make it through alone. You could say that I got through them because I worked hard, or just because believing in a higher power has some effect psychologically, or that there were coincidences involved, but when I put it all together, those reasons just don't work for me. But if I had to give just one reason that I believe God is real, it would be that He told me so. Audibly.

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2 pointseq ( 1 ) Study = not failed eq. ( 2 ) not study = failed add eq ( 1 ) & ( 2 ) study + not study = fail + not fail study ( 1 + not ) = fail ( 1 + not ) study = fail Then why should we study??

2 pointsthis one is pretty cute! Blonde v.s. Lawyer a lawyer sitting on a plane next to a Blonde want to pass some time and turns to her and says, "how about a trivia game, if i ask you a question and you get it right I'll pay you 10 dollars, and if you get it wrong you pay me 1 dollar. then you ask me a question, with the same conditions." blonde says, "no thanks, I'm reading a book." the lawyer says, "okay how about this, 20 dollars for getting right for you, and 20 dollars for getting wrong for me." the blonde rolls her eyes and says fine. the lawyer asks, "whats the distance from the earth to the sun?" the blonde hands him a dollar. then the blonde asks him, "what goes uphill with 3 legs and down hill with 4?" the lawyer blinks for a second and says " i have no idea, i guess you win that round." then hands her 20. "okay my turn again, i am curious, what does go up hill with three legs and down hill with 4?" the blonde hands him another dollar.

2 pointsWhat happens in quantum statistical thermodynamics stays in quantum statistical thermodynamics...b/c no one else cares.

2 pointsOut of the frying pan and on to the floor. Back into the frying pan, let hope none of the guests saw.

2 pointsI would think that the only way to make ANY sense of the situation is for the woman to repeat back to the croc EXACTLY what he said to HER: "If I guess right, you'll give my baby back, if I dont, you'll eat him. That's what you'll do to him." He'd have to return the baby, because she's CORRECT NO MATTER WHAT. Eh? hehehe

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1 pointThe answer should be 25. My "proof" is a brute force programming solution. I have a psuedocode c++ bruteforce solution. I can give the full version if requested. It takes a few seconds to brute force all possible paths. This might count as a proof, depending on if you trust the computer to be reliable. Basically what it does is it generates all possible paths, and then prunes as it goes along so the program dosen't take basically forever, or 6^27 moves. Now a proof will involve some theorems in graph theory, which I don't yet know all that well. Assume the XYZ plane void recursive_dumb_solution( A 3D cube,Position of X, Y, and Z of current spot,direction it went twice ago, direction it went to get here){ if traveled along a direction twice in a row, return to the above function. else if( x<0  x > 2  y < 0  y > 2  z < 0  z > 2) AKA if it exited the cube, return. else if(cube[x][y][z] == 1) AKA if visited spot already visited, then return. else{ //mark the current position of the cube as visited. cube[x][y][z] = 1; /////Moves in every direction possible. recursive_dumb_solution(cube, x+1, y, z, length+1,'x',prev_dir); recursive_dumb_solution(cube, x1, y, z, length+1,'x',prev_dir); recursive_dumb_solution(cube, x, y+1, z, length+1,'y',prev_dir); recursive_dumb_solution(cube, x, y1, z, length+1,'y',prev_dir); recursive_dumb_solution(cube, x, y, z+1, length+1,'z',prev_dir); recursive_dumb_solution(cube, x, y, z1, length+1,'z',prev_dir); cube[x][y][z] = 0; return; } }

1 pointHopefully this one has not appeared before... Suppose 27 identical cubical chunks of cheese are piled together to form a cubical stack, as illustrated below. What is the maximum number of these cheese chunks through which a mouse of negligible size could munch before exiting the stack, assuming that the mouse always travels along the grid of 27 straight lines that pass through the centers of the chunks parallel or perpendicular to their sides, always makes a 90 degree turn at the center of each chunk it enters, and never enters any chunk more than once?

1 pointGreetings, my name is Cody and I am new here in this forum. Nice meeting you all. Although I have never heard of it, I am actually quite curious about what it is!

1 pointTen years ago I called attention to a number that when divided by a single integer p it left a remainder of p1. (Help, a remainder is chasing me) Here is a chance to construct a ninedigit number, a permutation of { 1 2 3 4 5 6 7 8 9 } that has no remainders, sort of. The task is to permute { 1 2 3 4 5 6 7 8 9 } to create a number whose first n digits is a multiple of n for any singledigit n. For example, consider 123654987. Its first 2 digits (12) are divisible by 2. It's first 5 digits (12365) are divisible by 5. However this is not a solution, since 1236549 is not a multiple of 7.

1 point(BR / BL +UR) UL Thus... (8/4 +2) 3= 12 (2/1 + 6) 4= 32 (9/3 +4) 2= 14 and for the last one.. (6/2 +3) 5 = 30

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1 pointkbrdsk is correct: jasen's reply has error because more than two students would have spoken wrongly in each case: (Given: Exactly two students spoke wrongly.)

1 pointHi Jelly, and welcome to the Den. I searched on the Web a bit, and did not find puzzles of this type, but they may be out there. If anyone does find them, a link can be posted to this Forum: http://brainden.com/forum/forum/9othermindbogglingstuffonweb/

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1 pointSuppose you pick two random numbers less than n, then [n/2]2 pairs are both divisible by 2. [n/3]2 pairs are both divisible by 3. [n/5]2 pairs are both divisible by 5. ... (Here [x] is the greatest integer less than or equal to x, usually called the floor function.) So the number of relatively prime pairs less than or equal to n is (by the inclusion/exclusion principle): n 2  sum([n/p]2) + sum([n/pq]2)  sum([n/pqr]2) + ... here the sums are taken over the primes p,q,r,... less than n. Letting mu(x) be the mÃ¶bius function this is so the desired constant is the limit as n goes to infinity of this sum divided by n2, or sum(mu(k)/k2) (sum over positive integers k). But this series times the sum of the reciprocals of the squares is one, so the sum of this series, the desired limit, is 6/2. This number is approximately sum(mu(k)[n/k]2) (sum over positive integers k) 60.7927...%

1 point@plasmid Ignoring the reroll part and probability, rolling 2dice and taking the product does not create a uniform random integer. Some values will occur more often than others in that manner (1x4 & 2x2 both equal 4, e.g.),

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1 pointTo celebrate the Grand Opening of his new casino, kman offered the first 1000 patrons the opportunity to win some pocket change by playing a game that carried the catchy phrase Flip while you're aHead. Each patron paid $100 to flip a coin multiple times, winning $100 for every H (heads) that appeared, and stopping (without penalty) at the first appearnace of a T (tails.) What was kman's expected cost for this gesture of good will? A coveted bonanova gold star for an answer from the The Book.

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1 pointThis is incorrect because the minimum requirement only advances three months at a time. It does not suddenly jump forward by a year.

1 pointA retired gynecologist decided to become an auto mechanic. He was a good student and passed the final exam with flying colors. You are amazing, said the instructor, after the student had rebuilt an engine in record time. You mean no one else was able to rebuild an engine? asked the doctor. Of course, said the instructor, but no one else did it through the tail pipe!

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1 pointIt is 12MN when all the hands of this unusual watch rotates clockwise at proper speeds. But all the hands runs in opposite direction when they strike 12..like a pendulum. What is the real time if it reads false as shown below ?

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1 pointA mathematician and a Wall street broker went to races. The broker suggested to bet $10,000 on a horse. The mathematician was sceptical, saying that he wanted first to understand the rules, to look on horses, etc. The broker whispered that he knew a secret algorithm for the success, but he could not convince the mathematician. "You are too theoretical," he said and bet on a horse. Surely, that horse came first bringing him a lot of money. Triumphantly, he exclaimed: "I told you, I knew the secret!" "What is your secret?" the mathematician asked. "It is rather easy. I have two kids, three and five year old. I sum up their ages and I bet on number nine." "But, three and five is eight," the mathematician protested. "I told you, you are too theoretical!" the broker replied, "Haven't I just shown experimentally, that my calculation is correct! 3+5=9!"

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