A Classic from Logic

If you ever studied logic, you have definitely seen this question. I found it in Enderton though I'm not sure that it is originally from there.

You are in a land inhabited by people who either always tell the truth or always tell falsehoods. You come to a fork in the road and you need to know which fork leads to the capital. There is a local resident there, but he has time only to reply to one yes-or-no question. What question should you ask so as to learn which fork to take?

An easier question is: if you just wanted to figure out whether the resident was a liar or not, what would you ask?

"I love math and extra credit"

Here are the best to test doodle from my last math test. Enjoy.

Geek of the Week: Danica McKellar

Bringing glam back (or maybe "to") math. Not only does she have geek cred with the The Chayes-McKellar-Winn Theorem, but she is spreading the math love with her book, Math Doesn't Suck. I couldn't agree more.

Math Courseware Part 1--Hawkes Homework System

The math department, like most departments here at Tunxis, is eager to find ways that technology can help better serve our students. Our two main ventures are the use of MyMathLab in developmental courses and the pilot of two hybrid courses beginning Sping 09. We are not moving at blazing speed, but we want to make sure that we're not falling in the trap of tech for tech's sake. The following will begin a series evaluating different course management systems. It was put together by Steve Krevisky and Cora Preibis over at Middlesex Community College. Nice work guys!

Hawkes Homework System

Instruction:
• Has video lesson with audio. Lesson is mostly text
• Different levels of difficulty can be chosen by student to practice
• During practice, the student can ask for hint or step-by-step explanation
• Has mastery test after completing practice
• There are no hints during mastery, but student gets immediate feedback on question
• Textbook included, and can be used as a stand-alone product
• Interactive
• Drag and drop feature
• Has online grade book
• Has online test generator; tests can be downloaded

Technical:
• CD based – can be installed on home computer or network
• Lifetime license – need access code
• Has online grade book

Cost: Prealgebra – courseware and textbook $72 each.
Introductory and Intermediate Algebra $67 each
Combination Introductory and Intermediate Algebra $85 each

Strengths:
• Interactive and self-paced, but instructor can set due dates
• The student can have unlimited practice. He/she can choose to have a hint or see the problem worked step-by-step
• Instructor can create a diagnostics test online, and then download
• Can upload supplementary materials, such as course syllabus
• Has online grade book and progress report for student
• Focus is on mastery. The level of mastery can be changed by instructor
• There is a test generator available that can be exported into Word

Weaknesses
• Partly web-based and partly CD based. This may be a plus for some students without computers, but would probably create some difficulties for an online course
• The student must go online to submit grade for mastery test, while all of work is done offline
• The videos are mostly text, graphics are minimal
• Perhaps mathematics not rigorous enough (did not use parentheses with multiplication of a negative number)

LOOK FOR MORE SOON...

Going Up/Down

Here is a fun one to chew on.

Escalator Problem
Adrian is at the top of descending escalator, and his son Brad is at the bottom.
Adrian starts walking down the escalator, and counts 40 steps when he reaches the bottom. Brad starts running up the escalator, at three times the speed his father is walking down, and counts 72 steps when he reaches the top.
How many steps are visible when the escalator is stopped?

Post your answer when you get it. First correct answer gets 50 units of geek cred.

Seven, Seven, Seven

Rob sent me an email with a fun problem taken from a game show. Here it is

There are 7 girls in a bus.
Each girl has 7 backpacks.
In each backpack, there are 7 big cats.
For every big cat there are 7 little cats.

Question: How many legs are there in the bus?
We are warned: This is a real math problem so don't say that a bus has no legs.

It reminds me of the famous riddle (which actually made into a Die Hard movie) about the man going to St. Ives.

As I was going to St Ives
I met a man with seven wives
Seven wives with seven sacks
Seven sacks with seven cats
Seven cats with seven kits
Kits, cats, sacks, wives
How many were going to St Ives?

Thanks, Rob, for the problem. Everybody else keep them coming.

Slide Rule Sue Rides Again!

Sue brought her grandfather's slide rule in this morning. He was an engineer trained at MIT. Just being around it was seriously good math karma. Now if I could only figure out how to work it?