Pi Day Sudoku Is Back!

You laughed in 2008.

You cried in 2009.

This March, from the producers of Naked Sudoku*, comes…

PI DAY SUDOKU 2010!

As in past years, there is also a contest** associated with the puzzle, but who needs a contest when you’ve got a puzzle with the (conjectured) minimum number of clues (18 – in this puzzle, the first 18 digits of π) for a unique solution of a rotationally symmetric puzzle?  Here’s a printable PDF so you can take the puzzle with you to your next meeting lunch break.

Happy solving!

*Brainfreeze Puzzles, in case you were wondering.
**Also as in past years, we will not allow a solution to be posted until after the June 1 deadline.  Thank you for your cooperation.

Math in the 2009 Ig Nobels

The 2009 Ig Nobels were announced last week.  These are awarded “For achievements that first make people LAUGH then make them THINK”.    This year’s mathematics award is probably more of the think than laugh variety, however:

Gideon Gono, governor of Zimbabwe’s Reserve Bank, for giving people a simple, everyday way to cope with a wide range of numbers — from very small to very big — by having his bank print bank notes with denominations ranging from one cent ($.01) to one hundred trillion dollars ($100,000,000,000,000).

Poor Zimbabwe: we’ve talked about their  super-inflation difficulties and really big banknotes before.   They practically need their own category.

Most of the research is more amusing.   For example, the Peace Prize was given to Stephan Bolliger, Steffen Ross, Lars Oesterhelweg, Michael Thali and Beat Kneubuehl for their analysis of whether full beer bottles or empty ones caused more damage.  From their abstract:

Beer bottles are often used in physical disputes. If the bottles break, they may give rise to sharp trauma. However, if the bottles remain intact, they may cause blunt injuries. In order to investigate whether full or empty standard half-litre beer bottles are sturdier and if the necessary breaking energy surpasses the minimum fracture-threshold of the human skull, we tested the fracture properties of such beer bottles in a drop-tower.

(Short answer:  empties broke at a higher impact, which I think means they’re more dangerous.  I wouldn’t want to be hit by either one, though.)

But wait, there’s more.  Cows who give more milk when called by name.  A man who cracked the knuckles of his left hand — but not his right — every day for 60 years.  Giant panda poop as garbage disposal.  A bra that can turn into a pair of face masks in an emergency.  And my favorite, the Chemistry Prize, which went to Javier Morales, Miguel Apátiga, and Victor M. Castaño for creating diamonds from Tequila.

For all the winners, see the official site.

The Night Before Comps

Our seniors are taking their comprehensive exams, a department requirement for graduation, this weekend.  They’ve been studying for months (literally — we gave them the review packets last April and I know several people were working on them this summer) and now The Time Has Come.

Last week one of our seniors sent me this poem that she’d written in honor of the occasion, and she gave me permission to post it here.

Good luck everyone!

The Night Before Comps
A parody of Clement Clark Moore’s The Night Before Christmas
By Elyse Matson

’Twas the night before comps and all through Nazareth College,
The math majors were studying, stuffing their brains full of knowledge.
Notebooks and mechanical pencils scattered the room
In hopes that their proofs had the right “we assume”.
Coffee mugs nestled snug in their grips
With visions of scoring at least a 76.
With students in the library, and in the math center
Settling down for an all-nighter
When at one table there arose such a clatter,
The math majors looked up to see what was the matter.
Over to the commotion they went with a flash,
Someone was crying, sure she wasn’t going to pass.
The eigenvectors and values were giving her trouble
And she needed help with derivatives on the double.
When, what to the math majors wondering eyes did emerge,
A Solutions manual complete with p-series that diverge!
With step-by-step directions, and answers too
They knew in a moment they were going to pull through.
No more would they suffer from their torments,
They cheered and shouted and read the table of contents.
“On normal distributions and integration by parts,
On epsilon delta, and z-score charts.
To contrapositives! To proofs by induction!
Now integrate, integrate using u-substitution!”
As the students sat down and started to study,
The formulas made sense; they weren’t so fuzzy!
So question after question their mechanical pencils flew
Through linear, statistics, calc one and calc two.
Next the students began writing their proofs,
With enough “hence’s” and  “thusly’s” for their professors to approve.
After they took limits as n approaches infinity,
They stretched their legs and refilled their coffee.
Although sleepy and very tired,
They studied and studied doing all the questions required.
Their eyes – how they drooped! Their faces not so merry!
Their minds were fried, their stomachs empty.
Their problems complete, formulas whizzing through their heads,
The math majors went home to their beds.
And when they awoke to take their exam,
One of them uttered a not so quiet, “damn!”
“What’s wrong?” they asked, with concerned looks.
“We didn’t find out who sent us that book!”
The math majors asked around the college,
But couldn’t find a person to acknowledge.
After the exams were done and scored,
The students relaxed; they were glad to be bored.
And although, they never found out who helped them that night,
They all passed and got every question right!

Blue Man Math Contest

The Blue Men want you — yes, YOU — to use your mathematics skills for a contest! Well, if you’re a high school student that is.  They are inviting “high school science, performing arts, and math students” to enter a contest to create a musical instrument out of unusual items (for inspiration, think of the PVC pipes that they use in their performances).

But act quick — the deadline is January 15!  The official stuff is here.

Speaking of the Blue Man group, did you know that they opened an elementary school in New York City this past fall?  It’s called the Blue School and the classroom reminds me just a bit of one of their performances, although the $27K price tag is a bit out of my range (though apparently standard for NYC private schools).

Blue Man photo published here by Stefan-Xp under the GNU Free Documentation License.

2008 Putnam

The 2008 William Lowell Putnam Mathematical Competition officially took place this weekend! Yup, six hours of grueling math problems. We had a record number of students take it this year: 21! [That’s just 21, not 21 factorial. That would be an impressive number.]

Here’s one of the videos that our students watched while they were gathered around my dining room table Friday night eating dinner (because we totally bribe our students with food: dinner the night before at my house, bagels for breakfast, and lunch at the local pub in between the two three-hour sessions). It’s “I Will Derive” and I know it’s made its way around the internet, but I still think it’s fabulous:

And here’s the problem (A2) that caused the most discussion over lunch:

Alan and Barbara play a game in which they take turns filling entries of an initially empty 2008×2008 array. Alan plays first. At each turn, a player chooses a real number and places it in a vacant entry. The game ends when all the entries are filled. Alan wins if the determinant of the resulting matrix is nonzero; Barbara wins if it is zero. Which player has a winning strategy?

Here’s my favorite problem (A1) because I was able to solve it right away and do you know how often that happens? Not very.

Let f : R² -> R be a function such that f(x,y)+f(y,z)+f(z,x)=0 for all real numbers x,y, and z. Prove that there exists a function g : R->R such that f(x,y) = g(x)-g(y) for all real numbers x and y.

You can see the rest of the problems here, and pretty soon you should be able to find the answers here.  Edited Monday 12/8 to add: yes, the answers are posted!

No, of course Godzilla didn’t really use a calculator on an exam. He’s a stickler for following the rules.

Nominations for the 2008 Eddies

Here are 360’s nominations for the 2008 Edublog Awards:

Best New Blog: Division by Zero

Best Resource Sharing Blog: Teaching College Math Technology Blog

Best Teacher Blog: JD2718

Each of these three blogs is one we read regularly here at 360.  Check them out, and don’t forget to nominate your favorites by the 30th!

Olympiad Test Day Baby!

Today is the Second Annual University of Rochester Mathematical Olympiad, so in honor of the students at all the schools (including ours!) that are participating, here’s the math video that my students play before their exams.

Good luck everyone! And if you want to try your hand at some other contests, check out last year’s test or the Math contest problems link over on Wild About Math!

Scoring March Madness

This weekend marks the second weekend of the NCAA basketball tournament (aka March Madness). For many, the NCAA tournament is the last chance to watch some of the best college basketball around. For others, it’s a time to fill out brackets, decide which 10-7 upset to pick, flip a coin on the 8-9 games, and cross your fingers.

If you’ve ever participated in an NCAA office pool, you’re familiar with at least one way of scoring correct bracket picks. For example, each correct pick is worth 1, 2, 4, 8, 16, and 32 points, in the 1st, 2nd, 3rd, 4th, 5th, and 6th rounds, respectively. This makes each round worth the same number of points, and thus gives equal weight to each round. But is that the best way to do things?

When I was still in graduate school, several of us (looking for another way to kill time so as to avoid doing real work) decided to examine different schemes for scoring brackets. Not that we were participating in an office pool – just in case we ever wanted to join one. Or start one. Or run one for several years.

With the above scheme (1, 2, 4, 8, 16, 32), there are 192 points available in the entire tournament, and each round is worth 1/6 of those points, giving each round equal weight. This places a great deal of weight on the final game, and for whatever reason, we found that unacceptable. Of course, being able to determine the overall winner out of 64 (now 65) teams ought to be significant, but we didn’t want an incorrect pick to essentially eliminate someone from the contest. So we started analyzing other natural-looking sequences of length 6, computing the relative weights of each round for each sequence:

Points per game (Rds. 1-6)	Relative round weights (%)
1, 2, 4, 8, 16, 32	16.7, 16.7, 16.7, 16.7, 16.7, 16.7
1, 2, 3, 4, 5, 6	26.7, 26.7, 20, 13.3, 8.3, 5
1, 2, 3, 5, 8, 13	23.4, 23.4, 17.5, 14.6, 11.7, 9.5
1, 2, 3, 5, 10, 15	22.4, 22.4, 16.8, 14, 14, 10.4
2, 3, 5, 7, 11, 13	29.8, 22.3, 18.6, 13, 10.2, 6

Certainly there are other “natural” sequences that could be analyzed. We ended up choosing liking 1, 2, 3, 5, 10, 15 (although I no longer remember why). Perhaps it was a happy medium between schemes which weighted the final game too low (5 or 6%) and schemes that weighted it too high (16.7%). Regardless, we congratulated each other on an excellent nerding.

Later that spring, I discovered that Microsoft has an Excel template for scoring NCAA brackets, and I went berserk playing with it… but that’s a story for another day.

For problem-solving fun, see Monday Math Madness!

There are still a few more days to submit solutions to the first ever Monday Math Madness! This biweekly contest is being jointly sponsored by Sol on Wild About Math! and Quan and Daniel of Blinkdagger. The first problem was posed last Monday, and since the winner (of a $10 Amazon gift certificate!) is chosen randomly from the submitted good solutions there’s still time for it to be you — solutions are due Sunday night.

For details and the premiere problem, visit Monday Math Madness is here!.

“Double Down” Dumbs It Down

Double Down is a quiz show for New York State high school students that airs on PBS (WCNY to be specific). I happened to catch a rerun last night, and one of the categories was “Math”. Here are a couple of the questions:

1. A polygon with 5 sides is called what?
2. A polygon with 8 sides is called what?

These are high school students, remember. My 20-month old daughter knows what an octagon is. Can we give these kids some credit?!

Yes, I’m a Nerd

On a recent visit to my mom’s house (also the house in which I grew up), I was going through some of my old things (that is, I was asked to take them with me or throw them out) and I came across some math competitions I had taken in high school. (See, here’s the part where you say, “Wow, you’re a nerd,” and I reply, “See the title of this post.”) Specifically, I found two years of the American High School Mathematics Examination (AHSME, pronounced ahz-mee), and one of the American Invitational Mathematics Examination (AIME, pronounced ay-mee). My initial reaction was to recycle them, but something made me peek at the questions, and I ended up bringing them home, mostly to find out if I had any idea what I was doing back then.

It’s Putnam Saturday!

Today is the day of the 67th Annual William Lowell Putnam Mathematical Competition, offered all over the United States and Canada. According to the official website, Mr. Putnam was a strong believer in the value of team competition and so after his death his widow (Elizabeth Lowell Putnam) developed a trust fund which supported some intercollegial competitions. The first one was not in mathematics at all, but in English! The MAA took responsibility for the Putnam Competition after Mrs. Putam’s death in 1935.

Everyone who takes the Putnam these days takes it in two 3-hour blocks; the starting time, however, varies by Time Zone. Here in New York the times are 10am-1pm and 3pm-6pm. Are you an early riser? You might try taking it in at the Pacific coast, where the times are 8am-11am and 1pm-4pm. Are you a night-owl? Then head over to Budapest, perhaps on the Budapest Semesters in Mathematics, where the “morning” session runs 4pm-7pm and the “afternoon” session 9pm-midnight!

Websites with the problems usually pop up shortly after the competition is completed; websites with the answers appear a few days later. We’ll post links to those sites in the Comments as we discover them. Previous problems and solutions can be found here.