Milky Math Problems

Happy 19th, Milk of Random! (Whoops, uploading to WordPress belated, but live presentation was on time!)

(1) Ben Bitdiddle has one jug of milk. He then drinks one (1) jug(s) of milk. Excluding milk presently in his body, how many jugs of milk does Ben have now? Assume Ben does not have a pet polar bear.

(2) Solve the Diophantine Equation P=NP.

(3) The Milk decides to participate in a 100-smoot race. Unfortunately, it cannot run, and so it can only ooze. The Milk will be declared to have finished the race as soon as some part of it has oozed past the finish line. The milk begins with its entirety contained within the carton, and upon the start of the race begins to ooze milk out at a rate of one cubic millismoot per second. The milk then starts spreading horizontally on the ground in an expanding cylinder of ooze, with height one millismoot and circular base with radius expanding with the addition of milk from the carton. Assuming the carton stored an infinite amount of milk, at what rate would the radius of the cylinder of milky ooze have been expanding at the point at which the Milk finishes the race?

(4,5) Harvie the Aardvark just learned bogo-bogo sort. Thinking he could do better, he invents bogo-bogo-bogo sort. In bogo-bogo-bogo sort, one first randomly chooses two elements in the set, and runs bogo sort on them. Once they are succesfully sorted, one randomly chooses any three elements in the set (including possibly the ones already sorted), and runs bogo sort on them. One repeats this process with k elements, incrementing k by one each time, until k reaches the number of elements. If the set of elements is now sorted, the sort is done. Otherwise, reset and start over. Is bogo-bogo-bogo sort worse or better than bogo-bogo sort? If one comparison takes one second to perform and one swapping takes one second to perform, what is the expected amount of time needed to bogo-bogo-bogo sort eight elements?

(6) How many total injective relations exist from Simmons’ undergraduate residents to Simmons’ windows? Simmons has 340 undergraduates and 5538 windows.

(7) One Randomite is walking up the upwards-moving escalator at Shaws at 2 steps per second. The elevator itself ascends at a step every 2 seconds. A second Randomite decides to be more hardk0re and take the stairs. At each step, each Randomite has a one-half chance to decide to take a double-step instead (in the same amount of time it takes to take a single step). Find the speed at which the Randomite taking the stairs must progress to be expected to finish a flight of 36 stairs in the same amount of time as the Randomite using the escalator.

(8) A third Randomite decides to be even more hardk0re and ascend via the downard-progressing escalator. At each step, however, there is a 1% chance that the Randomite meets someone trying to go down the escalator, and thus has to return to the base of the elevator and wait for the now confused and/or annoyed shopper to ride the escalator to the bottom before starting again. At what speed must this Randomite progress to be expected to traverse the escalator in the same amount of time as the other randomites?

(9) Suppose that what the fox says forms a group of three-character strings under Caesar shifting, where if a=0, b=1, c=2, …, z=25, CaesarShift(a,b) is the shifting of each character in the string a forwards the amount treating b as a three-digit number base 26. What are all possible orders of this group of things the fox says?

(10) What is the smallest number of main buildings (buildings whose “numbers” are actually pure numbers without letter prefixes) that must be removed for there to be a Hamiltonian circuit through all of the remaining main buildings via the basement tunnels?

(11) Suppose that gay and lesbian couples could have biological children, and that one sex chromosome is chosen from each as is in the case of typical reproduction. Assuming all of a gay couple’s children are homosexual, what is the expected proportion of females in a gay couple’s grandchildren?

(12,13) (Two of) Paula the Painter, Sundance, and the Milk made a poor life decision in attending a party. After getting unreasonably drunk, they get convinced to participate in a game of circular cannibalism. That is, at one certain point in time, Sundance decides to begin drinking the Milk at 1 pound per minute, Paula decides to begin nomming Sundance at 80 pounds per second, and the Milk decides to begin engulfing Paula at 4 pounds per hour. Once each eater’s/drinker’s eatee/drinkee is fully consumed, the eater/drinker ceases further consumption. Each of the three also consumes their eatee/drinkee at a rate proportional to the amount of their body that is not yet consumed. Assuming Paula weighs 160 pounds, Sundance weighs 100000 pounds, and the Milk weighs 19 pounds, who ends up not completely eaten/drunk, and what percentage of the remaining entity remains uneaten?

(14) What percentage of Random Hall’s undergraduate residents could fit inside one small half?

(15) Architects decide that upon renovation of E52, the passageway that is supposed to line up with E62’s promenade this time probably should. In negligence, however, they now make above-ground connections to E53 defunct. Suppose that half as many people travel above-ground between E52 and E53 as above-ground between E52 and E62, uniformly distributed across the floors. In terms of floor transfers required due to going down to ground and going back to a floor, is this situation better or worse than before?

(16) As a contribution towards animal rights outreach, Shi Ke is making ties for hens. If hens are packed such that every point has at least four hens within a $\frac{\sqrt{2}}{2}$ radius of the point, and Shi Ke gave each hen one of four different ties, what is the smallest area inside which one can ensure that within the area are two hens wearing the same tie?

(17) What is the most random number?

(18) MIT’s Large Soul Colider (LSC) sucks a 50-kilogram soul at rest 50 meters away from a point towards the point using a force of 5 Newtons. At the point of interest lies a 100-kilogram soul. Assuming both souls to be perfectly elastic, at what velocity is the 100-kilogram soul traveling 5 seconds after collision?

(19) Ben Bitdiddle walked 5 miles south, 5 miles east, and 5 miles north, and returned to the exact location from where he started. Has Ben necessarily met a polar bear?