Spring 2017 POTW #1: Nadnerb's Course Schedule

Submissions due by midnight on Sunday January 29, 2017.

Welcome back to Puzzle of the Week, put on by the Emmanuel College Department of Mathematics! If you're new around here, you should know that we'll have a puzzle posted every Monday, with submissions due by Sunday night. You can earn points for your answers, and the top scorers at the end of the academic year (last week of April) will earn prizes.

Here is the first POTW for this semester, just a simple counting problem: 

It's the beginning of the semester, and Nadnerb is looking to fill his schedule. The Mathematics Department is offering 4 different courses, and the Philosophy Department is offering 5 different courses. Nadnerb has to take 4 courses, in total, and he wants to do so by taking either 2 or 3 Math courses (with the rest being Philosophy). How many different possible schedules could Nadnerb create? (You may assume there are no time conflicts between any of the courses.)

Results and prizes: 2015-2016 academic year

The results are in for the Emmanuel College Math Department's Puzzle of the Week contest for the 2015-2016 academic year! Congratulations to the individuals listed below for their outstanding performances with the variety of puzzles that I've posted over the last two semesters! Here are the standings, in order:

1. Darren Parke 
2. Paul Bleau
3. Pawthorne (?)
4. Rachel Gammal
5. Madison Daigle
6. Allison Mostowy
7. Connor Higgins

(Important note: I have no idea who Pawthorne is. Are you an Emmanuel student? Are you a group of people? What is your real name(s)? How can I contact you? I'm hoping you'll confirm your identity and claim a prize!)

Prizes were to be given out at our ceremony earlier today (which also saw the induction of three Emmanuel students into the Pi Mu Epsilon honor society) but not everyone was present. So, if you are in the top 5 listed above and have not yet claimed your prize, please find me in my office (Library G08-C) to pick up a fun math book from the list below. (These were all donated by Emmanuel Math Dept. faculty, so they are highly recommended, of course!)

• The New Ambidextrous Universe by Martin Gardner [already claimed by Darren] 
• The Artist and the Mathematician by Amir Aczel 
• Proofiness by Charles Seife
• Coincidences, Chaos, and All That Math Jazz by Edward Burger and Michael Starbird

I found it interesting that each of these books also has a substitle. So, to conclude the year with a fun "puzzle", try to match the book titles above with their subtitles below: 

• Making Light of Weighty Ideas
• How You're Being Fooled By The Numbers
• Symmetry and Asymmetry from Mirror Reflections to Superstrings
• The Story of Nicholas Bourbaki, the Genius Mathematician Who Never Existed

Spring 2016 POTW #5: Check (Your Work), Please!

Solutions due by Sunday, April 24, 2016.

This is the final POTW of the year! We will be awarding prizes for yearlong standings at an Emmanuel Math Department event at 4:30 pm on Thursday, April 28, 2016 (which is also Senior Distinction Day). At the same time, we will be inducting members of the graduating class into the mathematics honor society Pi Mu Epsilon. Emmanuel folks, please join us in celebrating the outstanding achievements of our seniors and you, the puzzlers!

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The 6 members of the Emmanuel Math Department recently went out to a celebratory dinner. When it came time to pay the bill, they discovered a few curiosities:

• Everyone except Brendan owed exactly the same amount for their meal.
• Brendan was an extravagant spender: His meal cost $10 more than twice the average of everyone's cost.
• Meanwhile, each other person's meal cost $10 more than half the average of everyone's cost.

What was the total bill for everyone, and how much did Brendan's meal cost?

Solution to Spring 2016 POTW #4 (Bow Do You Do?)

See here for the original post of the puzzle.

Let's say x is the number of administrators, so the number of faculty members is 2x.
Then, we can careful count all the bows that took place:

• Every administrator (x) bows to each other administrator (x-1): total x(x-1)
• Every administrator (x) bows to each faculty member (2x): total x(2x)
• Every administrator (x) bows to Sr. Janet (1): total x
• Every faculty member (2x) bows to each other faculty member (2x-1): total 2x(2x-1)
• Every faculty member (2x) bows to each administrator (x): total 2x(x)
• Every faculty member (2x) bows to Sr. Janet (1): total 2x

Total number of bows: x²-x+2x²+x+4x²-2x+2x²+2x=9x²
Therefore, 900=9x², so x=10.

This means there were 10 administrators, 20 faculty, and Sr. Janet in attendance, for a total of 31 people.

Spring 2016 POTW #4: Bow Do You Do?

Submissions due by midnight on Sunday, April 10, 2016.

At a recent college meeting, there were several faculty members, several administrators, as well as the President, Sister Janet. There were twice as many faculty members as there were administrators.

In addition, this was a rather formal academic meeting, so there were many bows that occurred: Every administrator made a bow to every other administrator, to each faculty member, and to Sr. Janet; also, every faculty member made a bow to every other faculty member, to each administrator, and to Sr. Janet. Overall, exactly 900 bows took place.

How many people were in attendance at this formal academic meeting?

(Use the submission box below to submit your answer. No need to explain: a correct answer will suffice for 10 points. However, feel free to explain your answer if you want a chance at some partial credit, in the event that your answer is incorrect.)

Solution to Spring 2016 POTW #3 (Stop, Clock, and Roll)

See here for the original post of the puzzle.

Since Clock A is gaining 1 minute every 24 hours, and Clock B is losing 1 minute every 24 hours, then the next time they will all show noon at the same moment will be when Clocks A and B both gain/lose (respectively) 12 hours (meaning they've gotten "closer together" by 24 hours).

Since they lose/gain 1 minute every day, and there are 12 x 60 = 720 minutes in 12 hours, then it will take 720 days to reach that phenomenon.

Thus, we are looking for the date that is 720 days after January 1, 2016. Be careful because 2016 is a Leap Year! So, the final answer is December 21, 2017.

Solution to Spring 2016 POTW #2 (Weird? You Bet!)

See here for the original post of the puzzle.

Trial and error may work here, but I don't recommend it. Instead:

• Suppose Adam starts with $A and Brendan with $B
• Adam loses first game, pays out to double Brendan's money.
• New results: Adam has $(A-B)$ and Brendan has $(2B).
• Brendan loses second game, pays out to double Adam's money.
• New results: Adam has $(2(A-B))=$(2A-2B) and Brendan has $(2B-(A-B)) = $(3B-A).
• By assumption: 120 = 2A-2B = 3B-A.
• Solve this system of equations to get A=150 and B=90.

Playing it out, just to check:

• Start: Adam has $150, Brendan has $90.
• Adam loses. New results: Adam has $60, Brendan has $180.
• Brendan loses. New results: Adam has $120, Brendan has $120.

(Here's a bonus challenge for you readers: Is there anything special about $120? Could this puzzle be solved for any ending amount? And what if there were 3 players and each one lost a round? Try to generalize!)

Spring 2016 POTW #3: Stop, Clock, and Roll

Submissions due by midnight on Sunday, April 3, 2016.

On this New Year's Day (January 1, 2016), at precisely 12:00 noon, I set up three clocks in my office. Let's call them Clock A, Clock B, and Clock C.

The next day, at precisely noon, I checked on them and discovered that Clock A had gained exactly 1 minute, Clock B had lost exactly 1 minute, and Clock C was right on time.

Assuming that the same rate of gaining/losing time continues on these clocks, When is the next date on which all three clocks will show precisely noon at the same moment? (That is, your answer should be a specific date, like "May 6, 2025" or something.)

(Use the submission box below to submit your answer. No need to explain: a correct answer will suffice for 10 points. However, feel free to explain your answer if you want a chance at some partial credit, in the event that your answer is incorrect.)

Spring 2016 POTW #2: Weird? You Bet!

Submissions due by midnight on Sunday, March 27, 2016.

Two players, Adam and Brendan, play high-stakes cribbage. They both entered with a certain amount of money, and they decided that the loser of a game should double his opponent's money. (For example, if Adam (with $10) lost to Brendan (with $6), then Adam would pay out $6 to double Brendan's money to $12, leaving Adam with just $4.)

Adam lost the first game, and then Brendan lost the second game, with each loser paying out according to the rule described above. After these two games and payouts, they miraculously discovered that both of them had exactly $120.

How much money must each player have started with, before the two games, to end up in this situation?

(Use the submission box below to submit your answer. No need to explain: a correct answer will suffice for 10 points.)

Solution to Spring 2016 POTW #1 (Vinyl Buys)

See here for the original post of the puzzle.

Say x and y are the costs of the two records. I bought them for x+y=100 dollars and then sold them for 1.2x+0.8y=110 dollars. (Note the 20% markup on x and 20% discount on y.) Solve this simple system of two equations with two unknowns and you'll find x=75 and y=25.

Spring 2016 POTW #1: Vinyl Buys

Submissions due by midnight on Sunday March 6, 2016.

Welcome back to Puzzle of the Week, put on by the Emmanuel College Department of Mathematics! If you're new around here, you should know that we'll have a puzzle posted every Monday, with submissions due by Sunday night. You can earn points for your answers, and the "top scorers" at the end of year will earn prizes. (But take notice: You can be a "top scorer" in terms of both high scores and frequent participation, so submit often and you may find that you've done better than you realized!)

To start the puzzling for the spring semester, here's a little algebra problem for you:

I collect vinyl records. I recently bought two valuable records for a combined price of $100. Later, I brought them to a record fair and ended up selling them both: one of them at a 20% markup and one of them at a 20% discount (compared to the original prices I paid). Overall, this netted me a $10 profit on the entire venture. What were the prices that I originally paid for the two records?

(Use the submission box below to submit your answer. No need to explain: a correct answer will suffice for 10 points.)

Solution to Fall 2015 POTW #6 (Ehhh, The Horror!) and #7 (Emmanuel Fay Cult)

See here for the original post for Fall 2015 POTW #6: Ehhh, The Horror!
Solution:

1. "The Silence of the Limbs"
2. "The Bards"
3. "2001: A Spice Odyssey"
4. "The Amen"

See here for the original post for Fall 2015 POTW #7: Emmanuel Fay Cult

Solution:

1. Yulia DEMENTIEVA (MEDIA EVENT)
2. Aren GERDON (GO NERD)
3. Christine LEIGHTON (HOTEL GIN)
4. Lenore MARTIN (TIN ARM)

Fall 2015 POTW #7: Emmanuel Fay Cult

Solutions due by midnight on Sunday, November 22, 2015.

Last week, the World Scrabble Championships happened in Australia. It just so happens that a few of my friends participated in the event and did very well! Specifically, congrats to Evan, John, Jesse, Dave, and Chris. They all placed in the Top 40 and deserve recognition; congratulations, all of you!

I used to play in Scrabble tournaments myself. The folks I met in that world have gone on to achieve marvelous things; in honor of them, this week's puzzle is based on anagrams.

Specifically, each answer here is the last name of a professor/lecturer at Emmanuel College. The names are clued by revealing a specific two word phrase which you must then anagram into someone's name. To help you, I have included the department in which the professor/lecturer works at EC, and I have tried to make the phrasal clues as transparent as possible (without being so revealing as to be uninteresting).

You may use the following website, which lists faculty at Emmanuel College, as a resource: http://www.emmanuel.edu/academics/our-faculty.html . Of course, you may use any other resource you wish, as well; part of the point of this puzzle is to get you to think and do some research. (Don't necessarily feel like you should be able to answer these questions off the top of your head!)

Keep in mind: Each clue reveals a two word phrase which then anagrams to the last name of someone on the list in the website link above; your answer should be the last name of the professor/lecturer clued.

For example, if the clue were, "This history professor has 2000 pounds of evergreens", the answer would be FORTIN since TON FIR anagrams to FORTIN.

I will award 2.5 points for each correct answer.

What is your name (or team name)?
(Please use the same name every week so that I can properly record your scores!)

(1) This math professor has caused TV and radio to report on a specific happening.


(2) This chemistry professor's rally cry might be translated as, "Huzzah, geek!"


(3) This education professor drinks a juniper liquor from a place where you pay for a nightly stay.


(4) This political science professor has a limb made from the element with atomic number 50.

Fall 2015 POTW #6: Ehhh, The Horror!

Solutions due by midnight on Sunday, November 1, 2015.

To celebrate this week's Hallowe'en Holiday, puzzle questions and answers are related to famous horror/thriller films. Every question/answer is based on a film on the American Film Institute's list of "The 100 Most Thrilling American Films". Feel free to use this list as a reference while solving these puzzles!

More specifically, the answer to each clue is a modified film title. Each title is obtained by taking the title of a well-known horror film (on that AFI list) and changing one of its vowels to a different vowel. (This is similar to a previous puzzle I posted.) I have provided clues in the form of brief synopses of the modified films.

For example, if the clue were "This war drama concerns young recruits and the steel outerwear they sport during October and November while the leaves change color", the solution would be Fall Metal Jacket. (Yes, Full Metal Jacket is #95 on AFI's "100 Years, 100 Thrills" list.)

Advice: look for references to both  the original and modified film titles in a clue.

Each correct answer earns 2.5 points. Happy spooky week(end)!

1. In this acclaimed film, a convicted killer (and former psychiatrist) helps an FBI trainee track a serial killer and keep his arms and legs quiet.
2. In this black-and-white thriller, a California town is mystified when Shakespeare, Chaucer, and other classic poets inexplicably rampage the citizens.
3. This Academy Award-winning film depicts mankind's relationship to the universe via apes, monoliths, an intelligent computer, as well as pepper, turmeric, cardamom, dill, cumin, and many more ...
4. A possessed child is the main antagonist in this 1970s horror classic, but in a climactic scene where his father drags him to an altar, the child only mutters a four-letter word signaling the end of a prayer.

What is your name (or team name)?
(Please use the same name every week so that I can properly record your scores!)


1.


2.


3.


4.

Solution to Fall 2015 POTW #5: Oh My Gourd!

See here for the original puzzle post.

Solution:

1. Pumpkin
2. Butternut (squash)
3. Acorn (squash)
4. Spaghetti (squash) ("Spa-Getty")

Fall 2015 POTW #5: Oh My Gourd!

Submissions due by midnight on Sunday 10/25.

To celebrate the autumnal spirit, this week's answers are all types of gourds and squashes. Each answer has been clued in a roundabout way, possibly involving a pun or wordplay and, at the least, involving an interpretational stretch. (In the parlance of crossword puzzles, these are "question mark-style" clues.)

Here's an example to help you: If the clue were, "Trigger that's pro-environment?", then the solution would be Green Button (which is a type of squash). (I promise the answers below are more well-known gourds and squashes...)

2.5 points will be awarded for each correct answer.

1. Relative of a particular kind of low-cut shoe?
2. Churning fanatic?
3. Maize doing well in school?
4. Place to get a mani-pedi owned by a particular American gas company?

What is your name (or team name)?
(Please use the same name every week so that I can properly record your scores!)


1. Relative of a particular kind of low-cut shoe?


2. Churning fanatic?


3. Maize doing well in school?


4. Place to get a mani-pedi owned by a particular American gas company?

Solution to Fall 2015 POTW #4: trivia with a theme

See here for the original puzzle post.

Solution:

1. Royale
2. The Middle East
3. Church
4. Great Scott

Theme: These are all live music venues in Boston.

Solution to POTW #3: MBTehhhhh

See this link for the original puzzle post.

Solution:

1. Haymarket
2. Government Centre
3. Braintree
4. Coolidge Corner
5. Cleveland Circle

Fall 2015 POTW #4: trivia with a theme

Submissions due by midnight on Sunday 10/18.

The questions below are straightforward trivia.

2 points will be awarded for each correct answer and 2 points will be awarded for identifying the unifying theme of the answers.

1.     According to Pulp Fiction, what you’d call a Big Mac (sans cheese) in France.

2.     A particular politically-contentious region of the world.

3.     A particular place of worship that has a pair of letters repeated twice (like the word mathematics does, with ma appearing twice).

4.     An old-timey way to say “OMG!”

What is your name (or team name)? *
(Please use the same name every week so that I can properly record your scores!)
This is a required question


Submit your answers for POTW#4 here *
This is a required question

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Solution to POTW #2: mOvie vOwels

See this link for the original puzzle post.

Solution:

1. Johnny Depp gives a stellar performance in this true-life tale of mobsters, the FBI, and the search for a deadly, dark-colored fungus.
   Black Moss (from Black Mass)
   
2. This critically-acclaimed Oscar-winner depicts the mayhem and violence caused by corruption, organized crime, and double-agents at a big city’s department of Citizenship & Immigration Services.
   The Deported (from The Departed)
   
3. In this dark tale of entangled crimes and accusations, a softball team’s enigmatic extra infielder is murdered by his childhood pal.
   Mystic Rover (from Mystic River)

Theme: All of these movies are set in the city of Boston, MA. (More specifically, they're crime dramas set in Boston, but I accepted "set in Boston" as sufficiently correct.)