BMAD

There is still a better answer

it can be done with calc or geometry. solution is still not the best.

At what time?

You have 2 different sized circles in a 2-dimensional plane. The smaller one is inside the larger with both centers at the same point C. The smaller circle can rotate while the larger circle is stationary. There are 3 different types of points: Type X, Type A, Type B. There must be at least 3 X points at the circumference of the smaller circle, evenly spaced. Type A and B points are put at the circumference of the larger circle as follows. A and B must be placed as a pair, A before B in a clockwise fashion, given a distance Delta apart (not arch length, straight line distance). There must be at least 3 pairs of A and B, but they do not have to be evenly spaced. However, each pair must be at least Delta distance apart. A CXA radius is defined as when an X point aligns with both point A and C (center) in which a line can be drawn to make a raduis of the larger circle. A CXB radius is defined as when an X point aligns with both point B and C (center) in which a line can be drawn to make a raduis of the larger circle. The object is to place the X points evenly spaced on the smaller circle and the A-B pairs on the larger circle such that, during a 360 degree clockwise rotation of the smaller circle there are always more CXB radii than CXA radii at any point of the rotation. What is the minimum number of X points, minimum number of A-B pairs and their locations (in degrees), and the radius of the larger circle if: Delta = .875"? Delta = 2.25"?

The smallest distance between any two of six towns is m miles. The largest distance between any two of the towns is M miles. Show that M/m . Assume the land is flat.

The minute hand of a clock is twice as long as the hour hand. At what time, between 00:00 and when the hands are next aligned (just after 01:05), is the distance between the tips of the hands increasing at its greatest rate?

A fair coin is tossed n times and the outcome of each toss is recorded. Find the probability that in the resulting sequence of tosses a head immediately follows a head exactly h times and a tail immediately follows a tail exactly t times. (For example, for the sequence HHHTTHTHH, we have n = 9, h = 3, and t = 1.)

The next sentence is true but you must not believe it The previous sentence was false

The last one escapes me for the time being :/.

Proof : 1 Clever Person = 1 mad person assume 1 clever person = 1/2 clever person + 1/2 clever persons ( if one person is 1/2 clever that means he is 1/2 mad ) = 1/2 mad + 1/2 mad = 1 mad. hence proved.

eq ( 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??

definitly helps to know what kind of questions people want...i mean why make questions that no one wants answered?

The claim is that any natural number can be completely and unambiguously identified in fourteen words or less. Here a "word" means an ordinary English word, such as one you might find in a dictionary. You know this can't be true. After all, there are only finitely many words in the English language, so there are only finitely many sentences that can be built using fourteen words or less. So it can't possibly be true that every natural number can be unambiguously described by such a sentence. After all, there are infinitely many natural numbers, and only finitely many such sentences! And yet, here's a supposed "proof" of that claim. Can you figure out what's wrong with it? The Proof: Suppose there is some natural number which cannot be unambiguously described in fourteen words or less. Then there must be a smallest such number. Let's call it n. But now n is "the smallest natural number that cannot be unambiguously described in fourteen words or less". This is a complete and unambiguous description of n in fourteen words, contradicting the fact that n was supposed not to have such a description! Since the assumption (step 1) of the existence of a natural number that cannot be unambiguously described in fourteen words or less led to a contradiction, it must be an incorrect assumption. Therefore, all natural numbers can be unambiguously described in fourteen words or less!

Theorem: It is possible to square the circle. Proof: Given: No mathematician has squared the circle. Therefore: No one who has squared the circle is a mathematician. Therefore: All who have squared the circle are nonmathematicians. Therefore: Some nonmathematician has squared the circle. Therefore: It is possible to square a circle. [QED] :-)

Suppose we have the fraction 19/95. To reduce this fraction simple cancel out the nines. 19/95 = 1/5 The cool thing is it doesn't matter how many nines we have on top we can always just cross them out and properly reduce the fraction (assuming that the 1 is preceeding the numerator and a 5 is following the denominator) for example: 199/995 = 1/5 19999/99995 =1/5 and so on... Same accounts for 16/64=1/4=1666...6/666...64 also 26/65 = 2/5, 266...6/666...65 = 2/5, and 49/98 = 4/8, and 499...9/999...8 = 4/8. and 16/64, 19/95, 26/65, 49/98 are all cases that satisfy a such property. And It is easy to prove! Have at it.

Object: to prove that i < 0 ( that is, sqrt(-1) < 0 ) ( .5 + sqrt(3/4)*i )^3 = (-1)^3 which means that .5 + sqrt(3/4)*i = -1 So then 1 + sqrt(3)*i = -2 sqrt(3)*i = -1 i = -1/sqrt(3) Therefore i is a negative number. QED.

Theorem: All numbers are boring. Proof (by contradiction): Suppose x is the first non-boring number. Who cares?

http://www.youtube.com/watch?feature=player_embedded&v=vLNOpoQztFo

http://www.youtube.com/watch?feature=player_embedded&v=52CzD31SqaM

$1 = 100 cents = (10 cents)2 = ($0.1)2 = $0.01 = 1c

I assumed that he was blind. Is he unable to see or does he put up blinds?