Heres 3 easy ones. 1. How many three cent stamps are in a dozen? 2. Barney Dribble is carrying a pillow case full of feathers. Hardy Pyle is carrying three pillow cases of the same size as Barney's. yet Hardy's load is lighter. How can this be? 3. Why are 1990 American dollar bills worth more than 1989 American dollar bills?
Here's one you might not know, again, from the site mentioned above. The second triangle is formed by rearranging pieces used to create the first. Yet there is a strange gap in the second triangle. Has area vanished? Is the conservation of matter bogus? Explain this madness. Please Register or Log in to view the hidden image! Absane probably knows this one though, as do most Math majors. Took me a while to figure it out initially. Nope. The father is just a device to further the riddle. He is of no import to the solution. Arkon got it. Here's another: The Tortoise challenged the great warrior Achilles to a 100 meter foot race, claiming that he would win as long as Achilles granted him a little head start. Achilles laughed, for he was a mighty warrior swift of foot, whereas the Tortoise was heavy and slow. "How long of a head start do you need?" asked Achilles, smiling. "Ten meters," said the Tortoise. Achilles laughs. "OK, you will most definitely lose, but we can race if you really want." "Actually, I will most definitely win, and I can prove it to you with a simple argument," said the Tortoise. "Go on then," Achilles replied, with less confidence than he felt before. He knew he was the superior athlete, but he also knew the Tortoise had the sharper wits, and he had lost many a bewildering argument with him before this. "Suppose," began the Tortoise, "that you give me a 10-meter head start. Would you say that you could cover that 10 meters between us very quickly?" "Very quickly," Achilles affirmed. "And in that time, how far should I have gone, do you think?" "Perhaps a meter - no more," said Achilles after a moment's thought. "Very well," replied the Tortoise, "so now there is a meter between us. And you would catch up that distance very quickly?" "Very quickly indeed!" "And yet, in that time I shall have gone a little way farther, so that now you must catch that distance up, yes?" "Ye-es," said Achilles slowly. "And while you are doing so, I shall have gone a little way farther, so that you must then catch up the new distance," the Tortoise continued smoothly. Achilles said nothing. "And so you see, in each moment you must be catching up the distance between us, and yet I - at the same time - will be adding a new distance, however small, for you to catch up again." "Indeed, it must be so," said Achilles wearily. "And so you can never catch up," the Tortoise concluded sympathetically. "You are right, as always," said Achilles sadly - and conceded the race. Was it really impossible for Achilles to win the race? Explain. Again, all from the earlier site. EDIT: Solutions to Arkon's riddles. 12 3 empty pillow cases are lighter than single pillow case filled with feathers. Because 1,990 $1 bills is $1,990.00 while 1,989 $1 bills is $1,989.00.
Three guesses: 1. a dozem 2. his pillow cases are empty 3. no dollar bills in 89? =P or they changed in that yr or something.
Good job Jaded. 1. Right 2. Right 3. Wrong, 1990 dollar bills are worth $1,990 while 1989 dollar bills are worth $1,989. Please Register or Log in to view the hidden image! Nice one Dapthar :Edit
I have no clue on both, maybe the shapes one, It just looks like you just move the shapes so you create the space.
lmao. because I read it wrong... again. Math is easier than English... I thought it said the person that crosses first wins... so I thought at that point, since their father died, either no one got the money, one of them did, both of them did, or someone else did... but whatever was written in the will (or what was not) can no longer be changed. oh well Please Register or Log in to view the hidden image!
Correct. Here's another: So, an eccentric entrepreneur by the name of Alphonse Null has sent out a press release about his new, mind-blowing hotel: The Hotel Infinity. Null informs the world that this hotel has an infinite number of rooms (specifically, an infinity equal to the cardinality of the integers). A quick tour puts skeptics' claims to rest; as far as anyone can tell, this hotel has infinite rooms. The consequences are mind-boggling, and Null sets up a press conference to answer questions... "So, Mr. Null, how will patrons get to their room, if their room number has, say, more digits than protons in the universe?" "The elevators have an ingenious formula device instead of buttons... simply input the formula for your room number, with Ackermann numbers or somesuch... your room formula can be picked up at the front desk. There's not even any need to know what the formula means!" "How do you produce the power and water for this hotel?" "I have infinite generators and wells, of course. This IS an infinite hotel, you know! *chuckle*" "What about costs? How much will it cost to stay here?" "That's the beauty of it! Since there are as many positive even integers as there are integers, I can change the same price to only every other room and still make the same profit! I could charge only every millionth room... each guest has a one-in-a-million chance of not getting a free room, and I still get paid the same! I love the properties of infinite sets, especially when it comes to profit!" "But, Mr. Null... I think you've made a severe mistake in your assumptions regarding profit..." "Oh?" The reporter then mentioned something which made Mr. Null's face turn white. "Oh... oh goodness... THIS PRESS CONFERENCE IS OVER!" Then he ran out. Assuming that everything Null said about the hotel is true: it really is infinite; it really is easy to get to your room; it really can generate infinite power for the guests; the cardinality of the set of multiples of a million, is the same as the cardinality of the integers... So with what simple assumption did Mr. Null go wrong? Note: "(There's one assumption I'm looking for, although any other assumption which would work is fine too.)" - Jeremiah Smith, writer of this puzzle. Again, from the aforementioned website.
There are not an infinite number of customers. (I am going to put this answer forward very boldly... though I assume I am wrong again because there is too much english involved).
Correct. Here's my final riddle for today: We know that the derivative of x<sup>2</sup> with respect to x is 2x. However, what if we rewrite x<sup>2</sup> as the sum of x x's, and then take the derivative: d/dx[ x<sup>2</sup> ] = d/dx[ x + x + x + ... (x times) ] = d/dx[x] + d/dx[x] + d/dx[x] ... (x times) = 1 + 1 + 1 + ... (x times) = x This argument shows that the derivative of x2 with respect to x is actually x. So what's going on here? Note: Most people with some math experience can show that some part of the argument is erroneous. As in simply, something doesn't follow. However, a full solution will explain why this argument attacks something that lies at the very heart of calculus itself, and that is what really explains why it's erroneous. To make it a bit harder for Absane, tell me what the more "fundamental" error is with this problem.
I'm lost.....do some easy ones! Please Register or Log in to view the hidden image! Please Register or Log in to view the hidden image!
Umm... step 1 is invalid If you say that x^2 = x*Sum(1,i=1 to x) = x+x+x+.. (x times), that is perfectly valid for positive integers only. If you were to graph that, you would be plotting points only so it is not a continuous curve. Since it is not continuous, the derivitive is not defined anywhere. I assume that is the fundamental thing you were talking about. Basically "Differentibility impies continuity" - the function is not continuous, therefore not differentiable.
Feeling philisophical? What's the begining of eternity, The end of time and space, The begining of all ends, And the end of all race? - N
I'm glad Absane knew the math one... my brain hurt from looking at the first step... *dizzyyy* Okay: You're in a room. This is a concrete room that has been built around you. The walls, ceiling and floor are about 4 meters thick and make of indestructable concrete... So you're pretty much trapped, yeah? In the room with you is: A Mirror A Table Using no logic whatsoever... and thinking in a surreal way... tell me, how do you get out? There is a correct answer...
