Weekend Edition Puzzle

While listening to NPR's Weekend Edition yesterday, I heard the following puzzle, which was created by Scott Kim:

Name five two-digit numbers that are evenly spaced out — like 32, 34, 36, 38 and 40 — in which all 10 digits from 0 to 9 are used once each. What numbers are these?

My son came up with one answer, which I thought was the only one, but when I gave it as extra credit to my students today as they were taking their exam I saw two other correct answers as well. Can you solve solve this puzzle? Can you come up with more than one answer?

After December 17, 2009 I will put the answers I am aware of in the comments section. No fair peeking until you've come up with a solution of your own! If you come up with one I do not have listed, please comment and let me know!

If you're looking for more of this sort of puzzle you may want to get ahold of Scott Kim's 2010 calendar called "Mind Benders and Brainteasers." AND BY THE WAY, if you are reading this before December 17, 2009, you can still submit your answer to NPR. Go to Weekend Edition at http://www.npr.org/templates/story/story.php?storyId=121382258 for details.

Math Proof About Happiness and Ham

Which is better, eternal happiness or a ham sandwich?

It would appear that eternal happiness is better, but this is really not so!

After all, nothing is better than eternal happiness, and a ham sandwich is certainly better than nothing. Therefore a ham sandwich is better than eternal happiness.


(Yes, this is mathematics. It is a "proof" using the transitive property, but you don't need to know that. You can just enjoy it as is!)

Mind Reading Three

The Prediction @ Yahoo! Video

Squaring Trick

Card Trick

Well, this is a "Fun Math" blog. Techincally this post is more on the "fun" side than the "math" side, but if you look at the comments section I do address that. For now, enjoy the trick!



Once you have made your selection click here to continue.

Spirograph Math

In order to create your own math SPIROGRAPH, click on the Mathematics Playground.

Amazing Moebius

This is a Moebius Strip in the creative work of M. C. Escher. A Moebius Strip has amazing properties. You can explore these by making your own Moebius Strip (without the ants!) quite easily. Take a strip of paper, give it a half-twist (turn one end over), and then tape the ends together. The result should look like the following:


Some things you might want to try are to put a dot in the center and trace a line along the "length" of the loop until you come back to where you started. Is this the same thing that would happen with a regular loop of paper? Now that you have a line along the center all the way around, grab a pair of scissors and cut along that line. Is this what would have happened with a regular loop of paper?

Much art, including sculpture by Max Bill and engravings by M.C. Escher have been based on the Moebius Stip and its properties. Stories have also been written, incluing "A Subway Named Moebius" by A.J. Deutch and "The No-sided Professor" by Martin Gardner.



And then there are the people who REALLY know how to have fun with a Moebius Strip, such as the creators of this video!

(Music by Didier Soyuz. Animation by Johnny Rem.)

Notice how the character goes around and around but is on top one time and bottom the other . . .

Conquering Chaos

Can you conquer chaos? To play the game click here.

In Fractal Geometry, "Chaos" can be used create amazing images. Rober Devaney of Boston University has created this game to help his students understand this process. To find out more about The Chaos Game click here. To find out more about the wild world of Fractals, explore his site, which the link takes you to - or just play the game and have fun!

Tessellate

A tesselation is a tiling of the plane so that there are no gaps or overlaps - like a tiled countertop. M.C. Escher used tessellations in much of his work. Some were pure tessellations, like the first picture below, others used a tiling that changed into something else, like the second and third pictures below. The following images are his works (for more see the official M.C. Escher site).

Shodor has a great interactive website where you can make your own tessellations with the help of a Java Applet. I used it to make the tessellation at the top of this post. You can change colors and can choose to begin with a triangle, rectangle or hexagon and can alter these shapes using their sides or corners. I started with a hexagon. The computer helps you alter them in ways that will fit together. Have fun!

Who is Your Role Model?

WHO IS YOUR ROLE MODEL?

Try this without looking at the answers......

Please don't look at the comments section until you do it, you'll love it I promise........no peeking?

GET A CALCULATOR (YOUR COMPUTER HAS ONE ON IT)

1) Pick your favorite number between 1-9

2) Multiply by 3 then

3) Add 3, then again multiply by 3 (I'll wait while you get the calculator....)

4) You'll get a 2 or 3 digit number..

5) Add the digits together

Now click on "comments" ..............

Note: I just got this email tonight - from a friend who claims not to like math! For all the people who say they don't like math it's amazing how many emails like this are circulating around out there!

MatheMAGIC

Click HERE to see a show by MatheMAGICIAN Arthur Benjamin.

Gifted?

Looks can be deceiving! Robin's REAL gift is with mathematics rather than with presents.

Click here to see her in action.

Can you figure out how she does this?

If you are in my Math 20 class and doing this for extra credit, see below for directions:

This is the final extra credit project for spring 2009. Try the trick. It should work every time. If you try it, and it isn't working, then you are not following directions correctly, so try again until you are able to follow the directions correctly. Then try it a few times to get a feel for how it works. Try to figure out what is going on. One approach is to look for a pattern. Can you figure out what gift she will say even without doing the math? What is she doing to make it work each time? A deeper question, that you need to answer in order to get all 10 points, is "Why does this work?" This is due on Thursday, April 23 at the beginning of class. Turn it in to my desk as you come in. GOOD LUCK!

Where Do I Stand?!

Many optical illusions have mathematics at their foundation. Speaking of a foundation, where is the one in this image? Some optical illusions have their roots in the "impossible shapes" created by mathematicians Roger and L. S. Penrose, as can be seen in the work of M. C. Escher who frequently used these shapes as a basis for his art. Click here to find an optical illusions slide show.

Results of Division by Zero

I have unsuccessfully searched for the creators of these. (The first and third are slightly altered forms of the originals.) Please let me know if you have any copyright information so that I can give credit to the artists.

Crazy?

Tear a piece of paper in half. Stack up the two halves. Now tear that stack in half and stack up the resulting four pieces. Now tear the stack of four in half and stack again. Imagine continuing to do this until you had torn and stacked 50 times. (Don't actually try to do this - the stack of paper gets too narrow and too thick, and you just can't.)


IF you could do this tearing and stacking 50 times, how tall would the stack be?

Assume that the paper is regular binder paper - about 0.003 in. thick (three-thousandths of an inch thick).

Just for the sake of argument, let me put it this way. The moon is about 250,000 miles away from earth. If someone said to you they thought this stack of paper would reach farther away than the moon would you think they were crazy? Would they be wrong? If they are wrong is it because their estimate is too high or too low? If they are wrong, how far off are they?

Comic Book Math

Tonight while I was at Border's with my friend Tammy, her son Noah was reading DC Comic Books. He found a riddle in one of them and tried it on me.

Here's the set-up. The supervillian Felix Faust tries to lead the readers to believe he can read their minds. He says the following:

"Choose a number between 1 and 50, but don't tell me what it is.
Add 8 to it,
then subtract 5,
then add 7,
then subtract 6,
and then subtract your original number from that result."

He is then able to tell you what number you get as your answer, even though he didn't know what number you started with!! Yikes! Should you fear the mind-reading powers of this supervillian?





But then one of the superheros from the Justice League of America pops up and reassures the reader that supervillian Felix Faust is not really mind reading but that it is just a trick and encourages the reader to try it on friends to see that it works every time.

What number did Felix Faust say you came up with?

Does it work every time?

Would it work for numbers bigger than 50?

Chocolate Math

I often get forwards like the following in my email, and I thought I'd share this one here.

Fwd: Chocolate Mathematics


Just got this and its too cute not to share. :-)

Subject: CHOCOLATE MATHEMATICS?

This is really cool..................and it really works!!!
ENJOY!
Pretty Cool, just give it a try!
You can check your math skills with
the below quiz.

CHOCOLATE MATHEMATICS

This is pretty neat how it works out.

DON'T CHEAT BY SCROLLING DOWN FIRST
It takes less than a minute.......


Work this out as you read. Be sure you don't read the bottom until you've worked it out! This is not one of those waste of time things, it's fun.


1. First of all, pick the number of times a week that you would like to have chocolate. (try for more than once but less than 10)

2. Multiply this number by 2 (Just to be bold)

3. Add 5. (for Sunday)

4. Multiply it by 50 - I'll wait while you get the calculator................

5. If you have already had your birthday this year add 1759.... If you haven't, add 1758..........

6. Now subtract the four digit year that you were born.



You should have a three digit number .



The first digit of this was your original number (i.e., how many times you want to have chocolate each week).

The next two numbers are ..........

YOUR AGE! (Oh YES, it IS!!!!!)





THIS IS THE ONLY YEAR (2009) IT WILL

EVER WORK, SO SPREAD IT AROUND

WHILE IT LASTS. IMPRESSIVE, ISN'T IT?

Mandelbrot Zoom

This looks like a piece of art but is a mathematical graph. Just have fun with it, though - watching the colors. Math can be beautiful!

Towers of Hanoi

To play the game you see below click here. It's called The Towers of Hanoi. A history of the game is given below the picture. When you go to the site where you can play it, you can choose how many disks to use, and you can also have the computer solve it for you if you get frustrated!



According to Math Around the World by Lawrence Hall of Science :

"The Tower of Hanoi (sometimes referred to as the Tower of Brahma or the End of the World Puzzle) was invented by the French mathematician, Edouard Lucas, in 1883. He was inspired by a legend that tells of a Hindu temple where the pyramid puzzle might have been used for the mental discipline of young priests. Legend says that at the beginning of time the priests in the temple were given a stack of 64 gold disks, each one a little smaller than the one beneath it. Their assignment was to transfer the 64 disks from one of the three poles to another, with one important provisonal large disk could never be placed on top of a smaller one. The priests worked very efficiently, day and night. When they finished their work, the myth said, the temple would crumble into dust and the world would vanish."

Truth or Dare!

Math isn't just numbers and shapes. It's logic too. The riddle in the video clip below from the movie Labyrinth is modeled after puzzles by logician Raymond Smullyan (whose books I highly recommend!!). Would you have figured out the right door to go through? Below the clip is a riddle for you to figure out. Good luck!




You are on a new reality TV show, you are the last survivor. You have dropped by parachute on a very bizarre island in the middle of the Pacific. There are two types of people living on this island, Northerners, who ALWAYS tell the truth, and Southerners who ALWAYS lie. You will win one million dollars if you can figure out the identity (Northerner or Southerner) of each of three people that you are presented with. If you cannot figure it out, you don't get the money, the program doesn't air, and you're left on the island for life.

The first of the three natives says something, but you don't hear it. The second of the natives says, "The first guy said he was a Southerner." The third native says, "Don't believe the second guy; he's lying. What the first guy said was the truth."

Who's who?

Math by Abbot & Costello

7 x 13 = 28
Right?!

Lou Costello of the comedy team Abbot and Costello can prove this three different ways.
Would you be able to explain to him why he's wrong?!
If not I guess you'll just have to accept that he is right!

Nim Game

To play the version of the game of Nim pictured below, click here. (Here is another interactive applet for Nim.) Nim is an ancient game. There are many ways to play. In some versions the person who takes the last object (or number) is the winner and in other versions that person is the loser. It is thought to have originated in China; the earliest references to Nim in Europe date to the 1400's. It is often played with whatever objects are at hand (pebbles, toothpicks, matches, coins), but it can also be played verbally, without objects, as desribed below.




In order to play Nim verbally, find a partner and choose a number that you will count up to. You also need to choose the maximum amount of numbers you can count off at a time. For example, let's say you and I are playing, and we decide to count to 21. We also decide we can say up to three numbers at a time. I might start by saying: "1, 2, 3," and you might then say "4, 5." I might follow up with "6," and you might say: "7, 8, 9." We could continue in this way until we got to 21, and the person to say "21" loses the game.

This is a great game for a road trip, and there is a very straightforward strategy for winning every time (no matter what the ending number or the maximum amount of numbers chosen). Can you figure out the strategy??

Impossible Triangle & MCE

This object is known the Penrose Triangle or Penrose Tribar, after Sir Roger Penrose, the mathematical physicist (and recreational mathematician who created it. Dutch artist M. C. Escher was interested in mathematics and used this impossible mathematical shape twice over to create his lithograph "Waterfall" in 1961. Can you see where and how it is used? After figuring that out, you might want to check out the wild video on YouTube posted below Escher's work.

Mind Reader 2

Check out the Flash Mindreader Page and see if they really can read your mind!

(At the site, if you scroll down, you'll see they've provided a place for you to do your work so that you don't even have to do it in your head!! How's that for a deal?)

The image at left is a lithograph done in 1935 by artist M.C. Escher, much of whose work uses mathematical ideas.

Mind Reader 1

If you want this guy to read your mind click on http://www.digicc.com/fido/

See if you can stump him. You might want to use your calculator to that you can work quickly and accurately.