# 2017 Pi Day Puzzle Hunt Recap

Imagine 150 teens sleuthing around the school solving puzzles, skipping lunch every day to gain advantages over other teams, students voluntarily solving extremely difficult puzzles.

Welcome to the Third Annual RMHS Pi Day Puzzle Hunt. This year 36 teams competed for \$200 in prize money, trophies and swag, and of course, GLORY. 🙂

There were eight challenging puzzles this year. A mural maze had students visiting other murals throughout the school in order to obtain the URL that gained them access to the next puzzle. The puzzles took students online, to classrooms, lockers, and making phone calls. Teams also received a UV light during the hunt in order to reveal secret messages (or cryptograms that still required decryption!). This year we did a better job of making the puzzles start out easy and slowly get more difficult, so as not to discourage teams right away. Here are links to descriptions of all of the 2017 puzzles:

Each year we have tried to improve the hunt in substantial ways, including the appearance of “Stars” throughout the hunt that earned students extra points by rewarding teams that could find hidden elements of puzzle or solve daily bonus puzzles. We also made the prize money and trophies better this year.

We had some bumps in the road, but overall, the 2017 hunt was a success. Months of work, and now our third puzzle hunt is in the books.

For more details, including photos, videos, and the puzzles, visit the Pi Day Puzzle Hunt Website.

See you next year, kids!

# Pi Day Puzzle Hunt

I’ll post more later, but here’s a sneak preview of this year’s Pi Day Puzzle Hunt. We’ve been working on this for months, and it finally happens next week. Here we go!

# When will she pass me for the first time?

[Guest post by Dr. Chase]

My wife and I walk on a circular track, starting at the same point.  She does m laps in the time that it takes me to do n laps.  She walks faster than I do, so m > n.  After how many laps will she catch up with me again?

Example:  For m = 4, and n = 3, she will catch up when I have finished 3 laps.  Reason:  When I have finished 1 lap, she finished 1 1/3 laps, so she is 1/3 of the track ahead of me.  (But hasn’t passed me yet.)  When I have finished 2 laps, she has finished 2 2/3 laps around the track, still ahead of me.  When I finish 3 laps, she has finished 3 3/3 laps, which is to say 4 laps.  So we are together for the first time since starting.  If m = 2, n = 1, she will catch up in just 1 lap.  If m = 7, n = 6, she will catch up in 6 laps.  Will she always catch up in n laps?  In how many laps will she catch up for arbitrary m and n?

# The first RM math assembly ever

Mr. Chase & Dr. Tanton

A math pep rally is how my administrator described it. So true!

We had a blast hosting Dr. James Tanton yesterday. (Thanks to the USA Science and Engineering Festival and its sponsors for making it possible!) This was certainly the very first “math assembly” in the history of Richard Montgomery High School!

James is a bold man, facing a crowd of 800+ teenagers with only a pen and paper. But his charismatic style was captivating. The kids loved it and I’ve been hearing only good things from all my students.

James talked about his own love for math and how he became a mathematician. He talked about how he was asking mathematical questions long before he ever actually declared himself a mathematician.

He taught the whole crowd the national math salute and, right from the start, he had us entertained!

When he was a kid, James would lie in bed and look up at the tiles in his bedroom and create little mathematical puzzles for himself. He challenged us to solve his puzzles too, and invited a few students up to try their hand at it.

We proved an interesting result with James, and unlike most of my proofs, he got a huge round of applause from hundreds of teenagers :-).

James gave our students a real sense of what it’s like to be a mathematician and do mathematical research–it’s a lot like playing! He had the students’ complete attention throughout the assembly and kept them very interested as he walked them through some fun problems and encouraged audience participation. They clapped and cheered for him. Like I said, math pep rally!

Afterward, James spoke with students who were enthusiastically bombarding him with questions, and he even got two autograph requests! (James = Rock star)

Afterward, some of the students and some math teachers had lunch with James. James got peppered with some more questions. Did you know his Erdős number is 3? Pretty awesome!

Thank you, James Tanton, for an awesome assembly!

# Soda Mixing Problem (revisited)

I posted a problem back in December that I never got back to answering. Sorry about that. The problem statement was:

Two jars contain an equal volume of soda. One contains Sprite, the other Coca Cola. You take a small amount of Coca Cola from the Coca Cola jar and add it to the Sprite jar. After uniformly mixing this concoction, you take a small amount out and put it back in the Coca Cola jar, restoring both jars to their original volumes. After having done this, is there more Coca Cola in the Sprite jar or more Sprite in the Coca Cola jar? Or, are they equally contaminated?

I have had the worked out solution for a while, just haven’t posted it until now. I’m relatively new with $\LaTeX$, but I’ve typed up the solution here, if you want all the gory details :-).  And yes, Peekay, you got the right answer!

# Who am I? (hint)

I posted the following problem back on December 3. I thought I’d post the solution, but then I decided maybe to just give you a hint. I’ve emboldened each true statement. The other statement in each pair is false. I did a lot of trial and error, making lists of numbers and crossing things off, narrowing it down. I didn’t have a great strategy, so see if you can do better. Can you figure out the number now?

There are five true and five false statements about the secret number. Each pair of statements contains one true and one false statement. Find the trues, find the falses, and find the number.

1a. I have 2 digits
1b. I am even

2a. I contain a “7”
2b. I am prime

3a. I am the product of two consecutive odd integers
3b. I am one more than a perfect square

4a. I am divisible by 11
4b. I am one more than a perfect cube

5a. I am a perfect square
5b. I have 3 digits