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.