BMAD

Three couples bought candy at a candy store. Each person paid as many cents per candy as pieces of candy he or she bought, and everyone bought a different number of pieces (no one was empty handed.) When they compared their bills, they found that the difference between the amounts paid by each husband and wife was the same. What is the smallest number of candies purchased? Show the amounts for the difference and for each person/couple. What if there were two couples? Four couples? Five couples? Can a method be extended for M couples? If the difference between each husband's and wife's amount is less than 500 cents, what was the largest number of couples possible in the store?

Given a set X with n elements, and sets A and B which are subsets of X, what is the probability of A being a subset of B?

Yragle the pirate has 100 white pearls and 100 black pearls. The white pearls are worthless, the black pearls are priceless. He will let you distribute the pearls between two sacks, labeled "Heads" and "Tails." After you distribute the pearls, you flip a fair coin and choose a pearl at random from the corresponding sack. How should you distribute the pearls between the two sacks to maximize your odds of getting a black pearl?

In complex analysis, an entire function is defined as a function which is infinitely differentiable at every point in C (for example: constants, polynomials, e^x, etc.). Picard's Theorem says that every nonconstant entire function f misses at most one point (i.e. f© = C or C-{x0}). For example, every nonconstant polynomial hits every point, and e^x misses only 0. Now consider the function f(x) = e^(e^x). Since e^x is entire, f is also entire by the chain rule. But it misses 0 since the base e^y misses 0, and it misses 1 since the top e^x misses 0 so that e^(e^x) misses e^0 = 1. But by Picard's Theorem there can be only one missing point, so the two missing points must be the same. Therefore, 0 = 1.

While my students are taking their final exam, i found myself playing with my whiteboard markers. I have 23 markers in all. One of my many habits is that I enjoy snapping my markers together to make long line segments. Unfortunately 3 of my markers will not snap together properly meaning that at best I have three line segments. therefore each line segment is considered a set marker length out of the total markers. E.g. a marker group of 17 markers has length 17/23. Now the question: If i create three marker lengths using all of the markers, and multiply the length of one line segment by the reciprocal of another by the MEDIAN marker length of all three for example: 1st marker group: 17/23 2nd marker group: 2/23 3rd marker group: 4/23 Median marker group: 4/23 17/23 * 23/2 * 4/23 what combination would give me the smallest value? largest value? Is there a process or means to generalize this for n markers?

While my students are taking their final exam, i found myself playing with my whiteboard markers. I have 23 markers in all. One of my many habits is that I enjoy snapping my markers together to make long line segments. Unfortunately 3 of my markers will not snap together properly meaning that at best I have three line segments. therefore each line segment is considered a set marker length out of the total markers. E.g. a marker group of 17 markers has length 17/23. Now the question: If i create three marker lengths using all of the markers, and multiply the length of one line segment by the reciprocal of another by the average marker length of all three meaning for example: 1st marker group: 17/23 2nd marker group: 2/23 3rd marker group: 4/23 average marker group: 23/69 17/23 * 23/2 * 23/69 = 391/138, approx 2.83 what combination would give me the smallest value? largest value? Is there a process or means to generalize this for n markers?

It depends on how you splice the question. essentially we could have one person play 1,000,000 and they will have a low but existing probability of being even. We could also have 500,000 people play twice and have again a low but existing probability of being even.

yay! finally got one.

on the right track!

this one breaks the op because it uses "floor command" and also sneaks in an implied (-1) but since you asked for a bad example, here you go: (floor(arccos(-cos(0))))! using the main branch of the arccos [0,pi].

Not necessary for B to know

Four heat-seeking missiles are initially placed at the corners of a square with side length s. Each missile flies at a constant speed toward the missile on its left. Describe the path each missile takes until it collides with the rest in the square's center. What is this path's length? What about five missiles placed on a regular pentagon? n missiles on a regular n-gon?

Given a coin with probability p of landing on heads after a flip, what is the probability that the number of heads will ever equal the number of tails assuming an infinite number of flips?

Alice-- i was driving on a highway recently for one hour at a constant and very special speed. Bob-- what was so special about it? Alice-- the number of cars i passed was the same as the number of cars that passed me! Bob-- your speed must have been the mean of the speeds of the cars on the road. Alice-- or was it the median? Bob-- these two are often confused. maybe it's neither? we'll have to think about this. Was Alice's speed the mean, median, or neither? Note: Assume that any car on the road drives at a constant nonzero speed of s miles per hour, where s is a positive integer. And suppose that for each s, the cars driving at speed s are spaced uniformly, with d(s) cars per mile, d(s) being an integer. And because each mile looks the same as any other by the uniformity hypothesis, we can take mean and median to refer to the set of cars in a fixed one-mile segment, the half-open interval [M, M+1), at some instant.

Consider a finite sequence of distinct integers. A subsequence is a sequence formed by deleting some items from the original sequence without disturbing their relative ordering. A subsequence is called monotone if it is either increasing (each term is larger than the one before it) or decreasing (each term is smaller than the one before it). For example, if the sequence is 4, 6, 3, 5, 7, 1, 2, 9, 8, 10, then 4, 6, 8, 10 is a monotone (increasing) subsequence of length 4 and 6, 5, 2 is a monotone (decreasing) subsequence of length 3. a) Find a sequence of 9 distinct integers that has no monotone subsequence of length 4. b) Show that every such sequence of length 10 has a monotone subsequence of length 4. c) Generalize. How long must the sequence be to guarantee a monotone subsequence of length n?

You have two 3-bit sensors, A and B, that measure the same thing, whatever it is -- temperature of the room, radioactivity levels, whatever. Both sensors are hooked up to the same CPU, which takes in the sensor readings. You know that the sensors are designed so that their readings can be off by at most one bit. We claim that if B knows that A has sent the CPU a 3-bit sequence, then B only needs to send 2 bits, and the CPU will be able to reconstruct B's 3-bit measurement, thereby conserving bandwidth. How is this so?

noodles

@PerhapsCheckITAgain I see no requirement that the numbers be square numbers just that i square three numbers

I have no idea who to give credit to for this one. team victory maybe??

Magical powers so that i can transport myself back and make up for lost time. Would you rather have a tiny wenis and be heterosexual or a giant wenis and be homosexual?