# Winner of the March PoTM

Better late than never, we wanted to tell you that the winner of the March Problem of the Month was Laurence White.  Congratulate him when you see him!

Don’t tell Laurence or Dr. White, but people named White are always trouble :

Maybe things would have gone better if Joe was a mathematician and/or listened to Mr. White:

Joe: He was the only one I wasn’t 100% on. I should have my f****** head examined, going on a plan like this when I wasn’t 100%.
Mr. White: [shouting] That’s your proof?
Joe: You don’t need proof when you have instinct.

# Problem of the Month: Examples Needed

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.

# Evolving Triangles!

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!

# Problem of the Month(s)

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!

# The Problem of the Month is Alive!

The Problem of the Month has just come out of a year long hiatus.  Don’t worry, though.  It was in suspended animation and is feeling better than ever!

You can find the problem on the math department’s webpage (just look for the Problem of the Month link).   Or click here to go to it directly.   In the non-virtual world you can find the problem and the rules in the display case on the 2nd floor of PHSC next to the elevators.

Not surprisingly,  November’s Problem of the Month is only open for business until the end of the month.   Get busy!

# November Problem of the Month

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.

1. There is one entrance, in the southwest corner, to a square room.
2. The dungeon extends infinitely to the east and the north, in straight lines from the southwest corner.
3. The rooms are rectangular, and arranged in east-west rows.  Call the southern most row the 1st row.
4. Each room in a given row has the same dimensions.
5. For n > 1, any room in the n-th row spans exactly two adjacent rooms in the (n-1)-st row.
6. There is a door between any two rooms with a wall in common.

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.

• (a) For each 2 ≤ r ≤ 10, what is the minimum number of doors you need to unlock?
• (b) What if r=100?

[See the rules in the PHSC 2nd floor display case for more information.]

# October Problem of the Month!

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.

1. The answer to this question is the average of the answers to all of the questions.
2. This answer to this question is the number of a question whose answer is maximal.
3. The answer to this question is greater than the answer to any subsequent questions.
4. The answer to this question is a question number whose answer is the number of this question.
5. The answer to this question is not the answer to any other question.

Bonus.  Determine all solutions to Steven’s Quiz.

[See the rules in the PHSC 2nd floor display case for more information.]

# September Problem of the Month

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.]

# A Summer Problem

Since the Problem of the Month is on summer holiday, we thought we’d challenge everyone to a problem out of the Pi Mu Epsilon Journal problem section:

Given a,b,c,d in the interval [0,1] such that at most one of them is equal to zero, prove that

$\frac{1}{a^2+b^2}+\frac{1}{b^2+c^2}+\frac{1}{c^2+d^2}+\frac{1}{d^2+a^2} \geq \frac{8}{3+abcd}$

– proposed by Tuan Le, student at Fairmont High School in Fairmont, CA

Good luck!

# April Problem of the Month

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.]