Hami, China

The city of Hami in China is also known as the city of Kumul in the province of Xinjiang. Hami is famous for its melons, but not much else. The Han people were in constant strife with the Xiongnu people over this region, as it was very fertile. When the Mongols invaded a small kingdom was established here called Qara Del. Benedict Goës visited on his travels through the area when he traveled to Cathay to see whether or not it was China.  Apparently, in the past the Chinese procured diamonds, gold and agate from this region.

Researched from http://en.wikipedia.org/wiki/Hami_City for Popsicle Stick Project #1
 

Lamarck vs Darwin on Woodpeckers

What would Lamarck have said about a woodpecker's cushioned head? And how would Darwin have replied? A hypothetical conversation:

Lamarck: Bonjour Charles!

Darwin: Cheerio Jean-Baptiste!

Lamarck: Ze woodpecker is a hard-headed old fellow no?

Darwin: Yes, thanks to natural selection.

Lamarck: Aah mon ami (shaking head dubiously). I say it is due to using his head over and over again to make holes in ze trees! He uses it and uses it and develops a cushioning layer from all this use. That cushion protects him. His little baby woodpecker inherits it from him no?

Darwin: Jean-Baptiste, you have made a mistake. The woodpecker inherits the cushioned head as follows:

Imagine a large population of woodpeckers. Some have well-cushioned heads, some have less-cushioned heads.

Woodpeckers with well-cushioned heads can peck holes in trees more effectively than woodpeckers with less-cushioned heads. This enabled the woodpeckers with well-cushioned heads to survive better during times of low food supply than their less-cushioned counterparts.

The woodpeckers with well-cushioned heads have a trait that helps them survive longer. This makes them more attractive to female woodpeckers. And as a result, they reproduce more.

Another anagram puzzle

What does IS PASSPORT RENEWAL scramble to that has 3 words, and the last word is SWANS?

Anagrams

Quick puzzle: How are these words, sentences, and groups of words related?

I DREW

IS PARADE

AA CRIME

(By the way, aa is a kind of lava.)

Answer: They're all anagrams! Anagrams are when you take the letters of any word or sentence and rearrange them to make a diffrent word or sentence.

Once you've solved the above, try this:
Unscramble the words below. (Hint: Sherlock Holmes)

(Clue: It has four words)

YEMEN

ELATE

DRY

MAR

NOT

SAW

2 little mathematical riddles

1. Imagine you have 100029 marbles.Your friend has 11(x) marbles, you don't know what x is.
You compare marbles and discover that your friend has "n" less marbles than you. What is "n" if it is less than 12?
2.10 brothers have had an extremely good apple harvest. The 10 brothers have divided up the crop evenly when one brother suddenly has to do an errand. The remaining 9 divide up the crop evenly again when another brother walks off again. This repeats until one brother is left with all the apples. Every time a brother walked off the apples were divided evenly, and every time the brother that walked off did not eat an apple. What is the least amount of apples where this is possible?

Mathematics...finally! (no.1: Cayley multiplication table)

(updated 2/5/13)
Several people (read:Dad and Mom) have been asking me if it's Math and Other Adventures, where's the math? I finally gave in and decided to start a mathematics column.
Thought #1: In mod n, the left diagonal of its Cayley multiplication table is a palindrome.
Mod (modular) is a system of arithmetic that is repeated. In other words, it goes round and round.
Ex: (mod 6)
012345
012345
012345
012345
012345
...
A number in mod is restricted between 0 and n. If it got larger, it would get reset back to the beginning.
Ex:
012345
012345
012345
...
Bold number 5 = 17

Now, here is a more succinct definition of modulus:

k(mod n)(that means k in mod n) = remainder of k/n

Here's why:
Imagine two sticks, a and b'.

Imagine b' is bigger than a.
Now say we cut off part of b' so there's a part b equal to a:

By definition, c is the remainder of b'/a.

But wait! If b is equal to a, b is equal to 0:(in mod a)
01234...a-1(because then total number of numbers is a)
0
(Bold 0 = b)
But that means that if you add c to 0, you get c! Therefore, c is what b' is in mod a. (This also works when b is a multiple of a, as multiples of a are 0 as well.)

Now, what is a Cayley table? A Cayley table looks like the below. This is a Cayley multiplication table,which is basically a multiplication table for modulus.

Now take a look at the left diagonal of this table:(next picture). As you can see, it's a palindrome (1410141).

Here's why:
The left diagonal is made out of squares(1,4,9,16,25,...) with the last square being (n-1)^2. Now, n-1is the same as -1 in mod n. n-2 is also the same as -2 , and so on. Around some point k is when x gets close to -x.
Now, we know that (-x)^2=x^2.
That means than (n-1)^2=(-1)^2=1^2,(n-2)^2=(-2)^2=2^2, and so on. This means that the values in the left diagonal's left side is mirrored by the values on the left diagonal's right side. But this means the left diagonal is a palindrome. So we have finally proven that the left diagonal is a palindrome.
Thank you for reading!
Dash

Note: Similar logic can be applied to find that the left diagonal and pandiagonals are palindromes.

A Little Mathematical Riddle

I sure seem to be in the habit of taking sabbaticals! :)

Imagine you are Chief of Police Montgomery, and you want to arrest the Rogerson brothers.
You want to know how many brothers there are, in order to fit them all in your prison cell. You can't see how many brothers because they have taken sanctuary.
You do, however, know 6 facts:

1. The Rogerson brothers' father, Peter, was a TzuTzuist. The TzuTzuists believe that you should only have a single digit number of kids.
2. Peter was extremely rich. His fortune was worth an eight-figure odd number.
3. The last digit of the fortune is 9.
4. The digit sum of the fortune is 17.
5. Peter divided the fortune evenly among his sons.
6. The fortune each brother received is a whole number.

How many Rogerson brothers are there? 

Frame puzzle 7

Dear Math and Other Adventures fans,
I (as usual) have taken another sabbatical, but I have started again!

Frame puzzle #6

Frame puzzle #5

Frame puzzle #4

Frame puzzle #3

Frame Puzzle #2

People find this one really hard!

The Daily Frame Puzzle (Frame Puzzle #1)

Hello, Math and Other Adventures fans! After a long sabbatical, I have decided to restart Math and Other Adventures.

I will start a new puzzle sequence called "The Daily Frame Puzzle". A frame puzzle is a picture. You are suppose to find out the word or phrase that the picture depicts.

Here's my first frame puzzle:

What does this picture say?

Solutions will be posted the next day.

The unilluminable room...illuminated (literally!)

You enter a room. It is dark. You cannot see, so you light a lamp that emits light through a tiny hole. You notice the walls are covered with mirrors.Suddenly, you realize there is still a part of the room that is dark. Wherever you go,this is true.Where are you? Your'e in... Tokarsky's unilluminable room!

Tokarsky unilluminable room was discovered by George Tokarsky in 1995, as a response to Victor Klee's problem. There are actually two rooms, a 26-sided one and a 24-sided one, both of which work.
My idea for making it illuminable is the following:
Take Tokarsky's room and turn it into a bubble wand. Take this, dip it in some soap, and run.
Tell your friend to take a picture of the bubble just before it comes out.
Place the match at the top of this dome, and Tokarsky's room will be illuminated!

Click here to see Tokarsky's room.

The Cloth Whizzer

Look out! Here it comes! Is it a bird? Is it a plane? No, it's the...Phd Classic Pocket Disc!

This toy is like a Frisbee, but better. It's made of cloth so if you're playing indoors, you don't have to worry about breaking anything. It's also extremely versatile, so you don't just have to play Frisbee, you can play golf, " Duck Huntin' " and " Ceiling Fan 500"!

Right now, I'm participating in two Phd competitions. I'm in the Best Game competition, where if I win, I get another Phd, and the Phd Name competition, where you think up of another way to spell "Phd"!

Click here to visit the official website.

The Sheriff Show

In what town does the town drunk lock himself in, the deputy sheriff has two girlfriends ( even though he isn't that smart and attractive), and the sheriff plays tricks on the deputy sheriff? Why, Mayberry, of course!

The Andy Griffith Show is about a sheriff called Andy Taylor (Andy Griffith) in a small, isolated town in North Carolina called Mayberry,along with his deputy, Barney Fife ( Don Knotts). Andy has a son, Opie ( the famous Ron Howard, though Ron is just a boy then,), as well. In the pilot, there are two housekeepers mentioned: Rose ( Mary Treen), of whom which just the wedding ceremony is shown, and Aunt Bee ( Frances Bavier), who is the new housekeeper. In the plot, Rose, Opie's favorite housekeeper, is getting married, and Andy calls up Aunt Bee, his old housekeeper. However, Opie isn't willing to give Aunt Bee a chance. And when she... But I won't spoil it for you.

Hope you like it!

Book Review: Moby Dick, Unabridged

Moby-Dick is about a famous "White Whale" and a captain's quest to kill him.

In Moby-Dick, the narrator, Ishmael (of "Call me Ishmael" fame,") goes to "explore the watery world", along with his friend, the "savage" Queequeg. Ishmael chooses to ship on the whaling ship Pequod, and he is told by the ship's owners that it is being captained by a certain Ahab. The owners,a certain Bildad and Peleg, also tell him that Captain Ahab lost a leg, and that it was "devoured,chewed up, crunched by the monstrousest parmacetty that ever chipped a boat". Also, Bildad is a bit pious, so he'll only give Ishmael the 777th lay(that's his share of the money) while Peleg wants to give him the 300th lay. In the end of the chapter, Peleg wins.

On the way back to their inn, they run into Elijah, a supposed "prophet", who warns them that they should not go on the Pequod. He says that everyone will die, but Ishmael takes no heed. Also, when he last meets Elijah, Elijah points out some men hurrying towards the ship and asks Ishmael "Did ye see anything looking like men going towards that ship a while ago?".

To find out what happens...read the book! It's long-winded and the author's research is mostly irrelevant but read it still. It's good for you!

A Mathematical Thought

I have just had an interesting mathematical thought, which I do not know the answer to.
Here it is:

I was watching a documentary called " The Story of Maths" hosted by Marcus du Sautoy, a documentary about the history of mathematics, and Marcus said that Euler proved that the infinite series 1/1+1/4+1/9... equals (pi^2)/6.
( My mother thought this very odd.) Anyway, my thought was this:
Supposed that you calculated all the results of all of these kinds of series ( thus, you would be calculating 1/1+1/8+1/27... and 1/1+1/16+1/81... and so forth.) My question is, is there a pattern between all these results? And if so, can you use this pattern to calculate the result for the next infinite series? ( that is, if you have the pattern and also have the result for the series before it, can you calculate the result of the series after it?)
Hope you enjoy this problem!

The Typing Game

Quick! Type "Quick"! Oh,no, not fast enough! But it's alright, you'll get another try.

What I'm talking about is Z-type. Z-type is a game where you have to quickly type a word that is falling towards you. If the word hits you, you will die, and you have to start all over again. If you manage to type it, you still have to contend with another word.
You'd be surprised how difficult it gets, especially in the later levels.

You have three types of words:
Disc shape: Easiest level.
Rocket shape: Medium level.
Unclassified shape: Hard level.

Hope you have fun!

The Green Light

Do you live in Sweden? If you do, then you probably know what I'm talking about. If you don't, don't worry, because I'm going to tell you right now. What I'm blathering about is the Aurora Borealis, and today, there was a specifically brilliant one above Stockholm. Witnesses say that it was" a gigantic display of dancing lights and Technicolor" and that it was an "absolutely awesome display" and that one would have to " lie on the ground to capture it all."
 Though this may sound nice, it's also worrying, because it signals that a particularly large solar flare is coming.Fortunately, NASA says that the ISS is fine. Unfortunately, there might be problems with communications and power grids, and also, all plane flights close to the Poles will be cancelled, because of the lack of communications. They will start back this Friday, because that's when the solar flare will stop.
Hope the flare doesn't cause you inconvenience!

I Love I Love Lucy

My new favorite oldies show is... I Love Lucy! Lucille Ball and Desi Arnaz are hilarious in this show of a famous bandleader and his rather odd wife. Living in New York City with their friends Fred and Ethel, Ricky and Lucy often get into bad situations, and their plans to stop it always backfire. A good episode is "Home from Europe", in which Lucy, after staying in Nice, France, gets some cheese for her mother, but when Ricky has to get on a plane quickly, and Lucy, due to plane regulations, is unable to bring it... well, I won't spoil it for you.
Hope you enjoy watching it!

Hilarious Volkswagen Commercials

Here's some hilarious commercials from the folks at Volkswagen!

The Rogue's Letter

Har Har Har Har! There's a new puzzle in town! Don't worry, my blog hasn't been taken over by hackers, I've just found a new puzzle! It's called The Rogue's Letter, and it's by Sam Loyd. In the Rogue's Letter, an international group of crooks have committed a great bank robbery. They are supposed to visit a series of 19 American cities, that are encoded in a letter. You, as the police, must decipher it.
This is the letter:
Dear Jim-I won the race. The track was at the Olympic level and hard as cobalt. I more than won, for my position was central-eight before and eight behind. They had all a start from a half to a mile-to them a considerable advantage, but I can win on a run or walk and overtake and meander by-or kill-the best of them. Treading from early day to night the roads we follow.ELLSWORTH.(End of letter.)
I am in the process of solving this puzzle (16 cities so far!) and I am hope that I will solve it soon.
Enjoy!

Coool Toool

Are you a kleptomaniac? Are you a government spy? Or do you just have an odd sense of what is fun?
If you're any one of these, then you have to go to TOOOL. TOOOL is "The Open Organization of Lockpickers", and teaches you how to pick a lock, how pin tumblers work, and much more besides.
Also, they have competitions, lectures, and "Lockpick Villages", where you can listen to mini-lectures and listen to shared lockpicker advice. There is some physics involved, so it's not purely for pleasure.
Hope you have fun!

My New Love for Hitori

I have found a new kind of puzzle called Hitori, which is quite fun.
Here are the rules:

1. The same number may not appear in any row or column more than once.
2. No two shaded squares may be adjacent.
3. The unshaded squares must be connected to each other (excluding diagonal connection).

Click here for some Hitori puzzles.

I Do My Duty; Other Things Trouble Me Not

From Philosophy for Kids, Question #4 -- Marcus Aurelius: Should you let little things bother you?

1. List some of these duties:
Duties to Parents (combining with Duties to Teachers, ahem!):
Annoy her, Study hard, tidy up, have fun, be nice, eat my vegetables.

Duties to My Friends:
Have fun, be nice, do not annoy them.

Duties to Myself:
Have fun, be nice, make a mess, read, study.

2. What is more important, doing your duty or trying to be happy?
Dash: Try to do both if possible.
Mom: What if you can't do both?
Dash: Then be happy.
Mom: :{

Discussion on Effort and Intelligence

From Philosophy for Kids, Question #3 -- Confucius: Should you be rewarded for your efforts in school?

1. What do you think Confucius is assuming about intelligence and also about the relation between effort and intelligence?

Dash: I think Confucius assumed that people have fixed intelligence. He assumed that no one cheats in a test. He assumed that if you put in a lot of effort, you are trying very hard to get the answer, therefore, you don't know the answer and have lower intelligence.

Mom: I think hard work can lead to high intelligence and that Confucius assumed effort and intelligence are two separate qualities and do not co-exist in one person.

A. Does intelligence vary from person to person?
Dash: Intelligence varies from person to person. But people can become smarter.
Mom: Agree.

B. Does one person's intelligence vary from subject to subject?
Dash: Yes. But you can improve if you study hard for that subject.
Mom: Agree.

C.Can intelligence increase, or does it remain the same?
Dash:. Yes., it can increase.
Mom: Agree.

2. Why should effort be rewarded?
Dash: You should reward effort because if you try hard, you can become smarter.
Mom: Doesn't that mean you are rewarding intelligence?
Dash: Effort begets intelligence.