Solution to POTW #1: the broken pocketwatch

See this link for the original puzzle post.

Solution:

We know the watch was correct at 2:00am. Let’s make a table of times, showing both the actual time and the time that the watch shows:

Actual time	Watch time
2:00 am	2:00 AM
3:00 AM	3:36 AM
4:00 AM	5:12 AM
5:00 AM	6:48 AM
6:00 AM	8:24 AM

Voila! When the watch stopped, showing 8:24am, it was actually 6:00am. Since that was one hour ago, it must now be 7:00 am.

“Alternative” method: We can take an algebraic approach instead of making a table of values and hoping to get lucky. Let X denote the number of hours that have passed since 2:00 am, when the watch last showed the correct time. Then, we can set up an equation that represents the time that the watch shows:

The left-hand side says, “The watch shows 8:24am right now”. The right-hand side says, “It was 2, and every hour that passed, the watch gained 1 hour and 36 minutes.”

Solving for X yields X = 4. That is, 4 hours passed since 2:00am, so the actual time was 6:00am when the watch showed 8:24am. Again, since it’s now one hour later, the time must now be 7:00 am.

POTW #2: mOvie vOwels

Due by midnight on Sunday 10/04/2015

The answer to each clue below is a made-up movie title. Each title is obtained by taking the title of a well-known film and changing one of its vowels to an “O”. I have given a brief synopsis of each made-up movie based on its title.

For example, if the clue were, “A caped crusader roams Gotham City thwarting criminals in the late hours, but he can be found playing Dungeons & Dragons and getting bullied by jocks during the day,” the correct answer would be The Dork Knight.

General advice: look for references to both the original title and the modified title in the synopsis. Also, remember that each example changes one vowel (A, E, I, or U) to an O.

3 points will be awarded for each correct title, and 1 point will be awarded for identifying the common theme uniting the films.

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.
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.
3. In this dark tale of entangled crimes and accusations, a softball team’s enigmatic extra infielder is murdered by his childhood pal.

Submit your answer via the Google Form below (or the link here):

What is your name / team name? *


This is a required question


Submit your answers for POTW #2 here. *


This is a required question

POTW #1: due Sunday 09/27/2015

Your pocketwatch is broken. Every hour it gains 36 minutes.
Exactly one hour ago, it stopped, showing the time as 8:24am.
You know that the clock showed the correct time at 2:00am.

What time is it now?

---

Submissions are due by midnight on Sunday 09/27/2015. Use the submission form below:

(link to submission form on Google Drive)

What's your name / team name? *


This is a required question


Submit your answer for Fall 2015 POTW #1 *
See mathpotw.blogspot.com for puzzle statement. Deadline: 11:59pm Sunday 09/27/2015


This is a required question

Never submit passwords through Google Forms.

Fall 2015 Puzzle of the Week is coming soon!

The new school year is underway and that means it's time for Puzzle of the Week!

I will post POTW #1 on Sunday 09/20 and submissions will be due by midnight the following Sunday.

Three new ideas that I will implement this year:

• Solutions will be posted the day after they're due. So, every Monday morning, I will post the previous week's solution as well as a new puzzle.
• Your submissions can be sent through this blog! This is the most exciting part. In the past, I've made you email me your answers. From now on, you'll be able to submit here.
• There will be prizes both for frequent participation and for overall standings. At the end of each semester, small prizes will be awarded for the students who participate the most often. At the end of the year (in Spring 2016), larger prizes will be awarded based on standings.

So, be on the lookout for a new post on Sunday! I suggest subscribing to this blog's feed or following me on Twitter @professorbrenda to get updates.