The Grand Poobah of the Problem of the Month has unleashed a new Problem. You can read the problem (and the rules) at the Problem of the Month webpage. It’s all about finding a certain bounded function.
If you can’t get enough of math pun comics, you’ve got to check out this webpage!
Don’t tell him, but we think the Grand Poobah of the PotM has bounded rationality.
You’ve probably already seen it on the second floor of PHSC next to the elevators, but we thought we should mention that the February POM is also posted online http://www.math.ou.edu/potm/.
Evolved Triangles from dirtytriangles.com
Also, a big shoutout to the winner of the Dec-Jan POM. Adam LaDine was randomly selected out of the correct entries. Congratulations Adam!
The POM Author (artist’s rendering)
In the hustle-bustle of finals, you may have missed that the Grand Vizier of monthly problems posted the December Problem of the Month. You can read it here.
Don’t be alarmed by the fact that December is more than half over, though, because this is also the Problem of the Month for January. So you have until the end of next month to get your solutions in.
Here’s the problem:
Four (shy) mathematicians are sitting around a table and want to know the average of their salaries. The problem is, none of them wants to reveal their salary to anyone else at the table. Is it possible to develop a scheme by which they can compute this average without spilling the beans on their salary?
Problem 1: Develop a scheme that our mathematicians can use to compute the average salary, without any one person knowing the salary of anyone else.
What if one of these four does not mind divulging his salary so that he is able determine the other three salaries, is it possible to construct a scheme to compute the average without revealing all the salaries?
Problem 2: Develop a scheme that the above mathematicians can use to compute the average of their salaries, without divulging the salary of anyone who wants to keep it secret.
– from the POM webpage
Just the thing to stimulate your mind while pretending to listen to your uncle drone on and on about who knows what during the family dinner!
It’s past that time of month again. Congratulations to October’s winner, Marli Sussmann! Now onto this month’s problem.
Darryl’s Dungeon and Dragon
Dastardly Darryl kidnapped the king’s wonderful wyrm. A melodious messenger readily recounted the darling dragon sadly starves in room r on the southern side of Darryl’s dungeon. Alliteration aside, your task, should you choose to accept it, is the safe return of the dragon. You are told the layout of the dungeon is as follows.
Once you enter, time is of the essence to get out with the dragon safely before you are caught. However, each door has a combination lock, which takes a while to crack, so you want to use the minimum number of doors possible.
Suppose you know the dragon is in room r of the first row. (We number the room you enter as room 1, the room directly east is room 2, etc.).
Problem.
[See the rules in the PHSC 2nd floor display case for more information.]
Congratulations to the winner of the September Problem of the Month: Thomas Morgan!
Now onto October’s:
Steven’s Self-improvement SSS
You need to start thinking about jobs, but your mother is worried that you’re not good at talking about yourself. Fortunately, she hears about Steven’s Self-Referential Aptitude Program in the OU Math Department. Unfortunately, it’s not what she thinks it is. Not knowing this, she makes you go see Steven to fill out an application. He gives you the following anti-entrance exam: if you can’t solve it correctly, you have to go through his program.
Self-Referential Aptitude Quiz
For each of the following questions, the answer is the number of a question.
Bonus. Determine all solutions to Steven’s Quiz.
[See the rules in the PHSC 2nd floor display case for more information.]
With a new school year, come new school problems. Fortunately, now you can forget about them and spend all your time on the new Problem of the Month!
Tomasz’s Tennis Test
(okay, it’s not a test, per say, but here it is)
Tomasz takes you to watch the US Open, but now its raining, and the matches are postposed until the rain lets up. Tomasz, fortunately, finds 4 cans of tennis balls and proposes a game. Each can holds 4 balls, and you put all 16 balls in a bag. Then you both alternate turns putting balls from the bag into the cans. On each turn, you can either place one ball back in a can, or two balls into the same can (provided they will fit). Whoever puts the last ball back in the cans wins.
Tomasz lets you go first.
Can you come up with a strategy that either ensures you will always win
or that Tomasz will always win?
[See the rules in the 2nd floor display case for more information.]
The Cathy Hall Show
Congratulations! You’ve just been selected to go on The Cathy Hall Show. On the set, there are three doors, and you are allowed to choose one. Behind one door is a car, behind another door is a goat, and behind another door is a cabbage, though of course you don’t know which is which. However, to help you, in front of each door is a TA who knows what is behind his or her door.
You can ask any TA what is behind their door any number of times you like (within the 5 minute time limit), and every time they will simply respond with either “car” or “goat” or “cabbage.” However one of the TA’s will always lie, one will always tell the truth and one will sometimes tell the truth and sometimes lie.
What is your best strategy to choose the door with the car?
[See the rules in the display case (PHSC, 2nd floor) for more information.]
While you’re stuck inside because of the snow, why don’t you think about some mathematical blizzards while sipping on your hot cocoa? Here’s the new problem of the month:
Here’s the new problem of the month, which can also be found on the 2nd floor display case of PHSC, with rules for submission.
Forester’s Floating Ferrises
Forester found that the fish in his pond like to ride ferris wheels. So he spends his Friday afternoons making floating ferris wheels. He makes 3 sizes of ferris wheels: 6 seaters, 10 seaters and 12 seaters. Each wheel is perfectly symmetric, so that the seats are equally spaced around a circle, and equally weighted so that the center of mass is at the center of the wheel when empty. (The weight of the base of the ferris wheel will not be important here.)
However, since the ferris wheels have a floating base, k fish can only ride an n-seat ferris wheel without it tipping over if they can sit in some arrangement of seats so that the center of mass remains at the center of the wheel (each fish weighs the exact same, and only 1 fish per seat).
Question. For each size of ferris wheel, determine the integers k such that k fish can ride the ferris wheel without tipping it over.
