Mathematical Trivia for Today

8/05/2015

MATHEMATICAL TRIVIA FOR TODAY:

Nine-Digit Pan-Digital Numbers (contain the digits 1 through 9 one time each, but they do not contain a zero).

The list below shows the smallest and the largest 9-digit pan-digital number that are divisible by the numbers 2 through 16.

Divisor	Smallest	Largest
2	123,456,798	987,654,312
3	123,456,789	987,654,321
4	123,457,896	987,654,312
5	123,467,895	987,643,215
6	123,456,798	987,654,312
7	123,456,879	987,654,213
8	123,457,896	987,754,312
9	123,456,789	987,654,321
10	There are none.	There are non
11	123,475,869	987,652,413
12	123,457,896	987,654,312
13	123,456,879	987,654,213
14	123,457,698	987,653,142
15	123,467,895	987,643,215
16	123,457,968	987,654,312

Source:

“Problem Solving Through Recreational Mathematics” by Bonnie Averbach and Orin Chein.

David

Surprise Appearance

8/04/2015

Surprise Appearance:

Suppose you have not lost all of your marbles.  Suppose you still have one bag that contains 10 marbles – 2 black and 8 white. 

I have two questions for you. If you draw the marbles out 1 at a time (without looking), which drawing is most likely to produce the first black marble?  Which drawing is most likely to produce the second black marble?

I think the first black marble is more likely to be  drawn out of the bag on the ________ drawing.

I think the second black marble is more likely to be  drawn out of the bag on the ________ drawing.

I will post the solution in a couple of days.

David

Brain-O Quiz Answers

8/03/2015

Answers to Last Fridays Brain-O Quiz:

1.  A towel.

2.  The other end of the rope was not tied to anything.

3.  66 + 66/6 = 77.

4.  There is no letter “e” in the paragraph, which is strange because “e” is the most frequently used letter in the English language.

5.  You would multiply with them.

Mathematics of Love and Sex

8/02/2015

Back in the day I used to imitate a high school mathematics teach and college instructor I used to list on the side of the chalkboard (or whiteboard) a list of the four or five main topics I needed to cover in the lesson for the day.  Sometimes I would list “Sex” at the bottom of the list.  Then just before we ran out of time one of the students would mention “Hey, we did not cover Sex yet!”

“Well, we are out of time – we will have to cover it in another lesson.”

That’s about all I know about the topic of “mathematics and sex” except some jokes about “multiplying”.

Well, that’s not quite true – I know babies come from Wal-Mart.  (Every Wal-Mart has a baby section.  Sometimes you will find a baby – all dressed up and mounted in a stroller – you know they sell better as a package deal.)  In fact, I decided to surprise my wife one day and found a cute baby at Wal-Mart (though I could not find the price or the bar code), but halfway to the check-out line I noticed a pungent smell.  I figured this baby was “out off date” or spoiled, so I put it back.  Nobody wants a spoiled baby.

I did check my Recreation Mathematics books and did not find any mention of “Mathematics and Sex”. 

Anyway, it too late to make a long story short.  I have run across two TED talks by mathematicians that also have books that will explain more that can be covered in a short TED video.

Sources:

“The Mathematics of Love” by Hanna Fry, and her TED Talk at: http://www.ted.com/talks/hannah_fry_the_mathematics_of_love#t-821375
“Finding the right mate is no cakewalk — but is it even mathematically likely? In a charming talk, mathematician Hannah Fry shows patterns in how we look for love, and gives her top three tips (verified by math!) for finding that special someone.”

“Mathematics of Sex” by Cleo Cresswell (University of Sydney), and her TED Talk at: http://tedxsydney.com/site/item.cfm?item=68C7E004B7DB49A6FB2E5953964C04D4
“Mathematics and sex are deeply intertwined. From using mathematics to reveal patterns in our sex lives, to using sex to prime our brain for certain types of problems, to understanding them both in terms of the evolutionary roots of our brain, Dr Clio Cresswell shares her insight into it all. Dr Clio Cresswell is a Senior Lecturer in Mathematics at The University of Sydney researching the evolution of mathematical thought and the role of mathematics in society. Born in England, she spent part of her childhood on a Greek island, and was then schooled in the south of France where she studied Visual Art. At eighteen she simultaneously discovered the joys of Australia and mathematics, following on to win the University Medal and complete a PhD in mathematics at The University of New South Wales. Communicating mathematics is her field and passion. Clio has appeared on panel shows commenting, debating and interviewing; authored book reviews and opinion pieces; joined breakfast radio teams and current affair programs; always there highlighting the mathematical element to our lives. She is author of Mathematics and Sex.”

David

For Mathematics Teachers Only:

8/01/2015

School is coming up soon and I have some tips that may eliminate some of the headaches you will get during the year

First, base your grading system on a million points instead of a hundred points.  This will eliminate you discussion about being "only half a point away from passing".  "But Bobby, you're over 5,000 points away from passing - I just can't curve your grade that much."

Second, don't argue about whether students can use calculators on tests and quizzes.  Just re-write you tests to include only numbers with at least 12 significant digits.  (Warning: This won't work if the student has a TI-89 calculator.)

Third, allow all students to turn in homework late - no mater what the excuse is.  Tell them to sign up for your course again next term, and they can turn in their homework at that time - and you will give them full credit.

Fourth, don't worry about typos or proof reading your tests, and you can still use multiple choice tests!  Just add another answer for each question: "E:  None of the answers above are correct.  The correct answer is (fill in the blank).  (Please remember, the answer needs to be be accurate to 12 significant digits!)"

Rent a "Robo-Call Machine" and program it with each parent's phone number.  "Johnny did not complete or turn his his homework today.  Please complete his homework assignment for him and bring it to the school before the end of the school day.  Thank you."

Add statements to at least half your report cards saying: "Though Johnny is having difficulty at school, testing indicates that he might excel in a a home schooling environment."

Finally, if you are the kind of teacher that occasionally assigns "write offs" - continue to do so.  Have the student write: "If I could come to class on time and prepared, take notes during class, and do all of my homework and turn it in on time, then I would almost certainly be able to pass all of my tests."  Just assign 10 of these to the student.  But assign 90 of these to the parent: "If I would teach my son or daughter to be on time ... " etc., etc., etc.

I hope these simple tips will help get your year off to a smooth start.



David