Here you are the solutions for the secon day exercises :D

I very much hope you have interesting plans for this forthcoming week before we get back to class ^_^ And don't forget you have an ordinary challenge and the possible faces for Euler Piruleta in the 2 previous entries :)

Happy New-Sierpinski Year!!

These are some wonderful choreographies by the American band "OK Go". I even danced once one of them with some friends XD So if you have some spare time... enjoy!!

I very much hope that Olentzero/Apapalpador will bring you everything you deserve (should you don't deserve anything, please, try harder througout 2013 XD )

Best wishes and see you soon!!!!

PS: This is an "ordinary" challenge for these Christmas days :D It is quite interesting!! You'll find out! Deadline: January the 10th.

Euler Piruleta vs. Cell
and his Plans for conquering Spain

Poor
Daleks… they have been defeated once more thanks to your invaluable help! Although
Euler Piruleta surely deserves to take some free time, threatens to our beloved
planet won’t stop… What a restless life!!

This
time, Cell, who has recently
absorbed those 3ESO-Bilingual-Program-students whose necks have red marks from
previous absorptions by boy/girl/pet-friends, is planning a strike against Spain. Some of his former victims were Angel, Iñigo and Miguel... We all know they were in SUCH pain... XD

To
prevent this attack, Euler needs to regroup all the regions in Spain
in a way such that:

-The regions in each group have no common
borders.

-The least possible number of groups is
used.

Our
hero is quite frightened since he doesn’t seem to know the least number of groups with the property that the regions in each group
have no common borders.

Can
you help him?

Use the map below to get the solution. How
many different colours would you need to colour Spain’s map noticing that you can’t
colour two frontier regions with the same colour? You must use the least possible number of different colours!

Your solution must include
the least number of colours needed and a coloured map of Spain
supporting your decision.

Mathematical background:

This
story stars in the XIX century…One shinny morning of 1852, Francis Gutrhie asked himself about a
problem he had been thinking of… How many different colours would be needed to
colour a map without two frontier countries having the same colour?

He reckoned what he thought would be the correct answer, but he also
found himself unable to prove it. At this point, he decided to ask one of the
greatest mathematicians of that time: Augustus
de Morgan, who also didn’t manage to find the solution.

We had to wait until 1977 when Appel
and Hacken gave a proof based on
computers simulation.

Finally Euler has been granted some days off... But he has left us some homework!! OMG! So cruel our Euler Piruleta...

1) First assignment: You have to vote for Euler Piruleta's face! These are our four options:

Send an email to hausdy@gmail.com. Give 4 points to the one you prefer, and then 3, 2 and 1 for the rest!

2) Second task (real homework):These exercises should be done by the 8th of January. Don't forget to bring them to class the first day after Christmaaaass!! Solutions will be uploaded every weekend with interesting facts and a new ordinary challenge... who will Euler Piruleta fight after his holidays?

3) The Greatest Challenge so far: Origami's Twisted Tower! Remember, if you manage to complete your own tower, an extra point will be added to your second term global exam (what implies +0,4 points in your final second evaluation mark!) The instructions are below (the video + some pictures)

Most of you have done an impressive job with this exam :D

However, there are still some T-E-R-R-I-B-L-E mistakes which will eventually exterminate you by the Daleks or even worse... by ME!! :P

REMEMBER!

$2 \cdot \frac{3}{2}$ is equal to $\frac{6}{2}$ and not to $\frac{6}{4}$ ¬¬ ejem ejem...

AD01

8,6

BC01

8,8

AD02

8,8

BC02

5,9

AD03

9,2

BC03

8,8

AD04

7,9

BC04

8,9

AD05

8,2

BC05

9,8

AD06

7,5

BC06

7

AD07

8,2

BC07

4,4

AD08

7,3

BC08

7,1

AD09

7,1

BC09

9,9

AD10

8,7

BC10

8,9

AD11

6,6

BC11

6,6

AD12

9,3

BC12

4,6

AD13

9

BC13

4,3

AD14

10,5

BC14

9,8

AD15

6,6

BC15

10

AD16

9,7

BC16

8,9

AD17

2,8

BC17

7,2

AD18

6,1

BC18

7,9

AD19

10,3

BC19

5,7

AD20

9,1

BC20

7,6

AD21

5,7

BC21

4,7

AD22

7,2

BC22

9,3

AD23

9,2

BC23

6,6

BC24

8

Did you know that the man who introduced the "Futbolín" in Spain was Alexandre de Fisterra from Galicia? We owe so much to him :D There's even a song from a TV Program ("O Xabarín Club") which was remarkably famous when I was 12 years old :P

Finally
Euler Piruleta has retrieved his face which will be made public throughout this
week.

Nevertheless,
his challenges haven’t stopped yet and once again he is about to face the most
hazardous situation…

Although
their presence may be terrifying, they don’t have the smarts, so the challenge
they have come up with is not that difficult to understand.

Read carefully the message the Daleks have sent and
try to solve the mysteries they have stated… Only if you wish to survive to
their conquer attempt, otherwise prepare to surrender and be treated as a Dalek
Slave for the Cult of Skaro!!!

“This is DalekKan
speaking. Prepare to surrender. Fighting is pointless. The Daleks will be the
masters of the universe. Your only chance to survive is figuring out how to
divide this figures as requested. Otherwise, you will be.......

E-X-T-E-R-M-I-N-A-T-E-D!!!

Part I: Try to divide the following geometric
figure in 4 equally shaped parts.

Part II: How many different ways can you come up with to divide a square into 4
equally shaped parts? They
must have not only the same area, but the same shape as well (Originality will
be taken into account!!)

Watch it: you
can either deliver the solution by mail or by the old-fashioned mean:
handwritten. Euler Piruleta will really appreciate your help!!

Deadline: Thursday the 20th. Printable version HERE!

This song may help you to relax and focus on your endeavour to solve these challenges :) Each one of them will be rewarded with one extra possitive!

Poor
Euler Piruleta... he has forgotten how his own face looks like! Due to this
problem he has started a never-ending quest to retrieve his face.

Nevertheless, it
seems that evil forces have spelled a cast on him and he has been trapped in
what looks like an endless quest... Oh no! He is cast away in a Möbius Strip!

If you wish to
help Euler Piruleta, you should know one or two things about this "Möbius
Strip":

1) The Möbius
Strip is a peculiar surface with intriguing characteristics.

2)
Every surface that you know has two faces (a sheet, a coin, the floor...) but
the Möbius Strip has just one face... an endless face!

3)
Unfortunately for him, our poor Euler Piruleta doesn't know these properties
and that's why he needs your assistance…

1)Build your own
Möbius Strip.

You
just need a long (and at least 4cm-width) paper strip.

Glue one end to the other as it is depicted in
the image below, turning one end:

Is
it possible to paint the inside and outside of the Möbius Strip using different
colors? Why?

2)Cut your Möbius
Strip in two (following an imaginary line which should be drawn exactly in the
middle of your strip):

Once you are
done… what do you get?

How many “turns”
does the object you have created have?

3)Repeat the
procedure you have done in the previous step and describe what you get.

Only if you
fully understand the complexity of the Möbius Strip will Euler Piruleta be
released from his infinity prison.

Watch it: your
solution must include pictures of the outcomes of every part: your original
Möbius Strip, the one you get after the first cut and what you get after the
second cut.

For amusement only: this was another endless quest that become quiet famous when I was in school!

Dragon Ball Opening - GALEGO's Version

PS: Tania, Iván, Carlos, Andrea I., Jorge and Iñakig G. have been awarded with TWO possitives due to their answers to the last challenges ;) Congratulations. Euler Piruleta is starting to be very fond of you :P

Forever Alone has given up his will to expend the whole eternity alone and has decided to take every single kid studying 1st or 2nd of ESO, among whom there are some of your siblings...

Damnable!

The instructions he has given to set them free are the following:

1) I promise half of them will be released if you solve the following simple challenge:

The snail's journey

A
forever-alone-snail has fallen into a 12-meter deep pit. Lucky him, this
pit was not filled with water, otherwise this fellow snail would be
forever-alone dead.

After two days
waiting for a rescue, he makes up his mind and decides to try to get out of the
pit single-handed. During the daylight, he manages to climb 2 meters, but when the
night time arrives, he rests and therefore slips 1 meter backwards.

How long will it
take for the snail to reach the surface?

2) All the hostages will be released if your brain manages to sort out the following situation:

The Three Hats

Three
forever-alone prisoners have bribed the guard to let them run free. However,
when the time comes, the guard decides to add one extra challenge: “I have here 5 Mexican
hats: 2 black hats and 3 reddish ones. You will be set
in a single line and three hats will be put over your heads. This way, the
person standing at the back can see the second person and the first one (and therefore
their hats), the person who is placed in the middle only sees the person
standing before him (and his hat) and the first one can’t see anybody. Some questions
will be asked and your freedom depends on some of you to give the right answer.
In the event of failing all the questions, you should be here forever and
forever-alone with me”

The guard
started:

-“This question
if for the guy in the back”. What’s the colour of your hat?”

-“I don’t know”, the prisoner replied.

-“OK. You, the
second one. What’s the colour of your hat?”

-“I don’t know”, the prisoner replied.

-“Muahahaha!!!!
You’re bound to be here with me for all the eternity!!!! Last chance! You, the
first one, will you be able to guess the colour of your hat?

-“I have a red hat”, she stated.

And
the prisoners were released.

How did the prisoner in the first
place of the single line guess the colour of her hat?

"This are the challenges you have to face. Shall my commands not be met, a disaster beyond your imagination will occur"

Euler Piruleta's services have been required once more to try to fight the maths terrorism!! But he needs your help!! Each challenge will be rewarded with one positive but be careful, Forever Alone's deadline is November the 18th... Do not hesitate and help Euler Piruleta to release the children!

Will Euler Piruleta manage to defeat evil Forever Alone? He has decided to relax with some music before the struggle:

(Rebecca Black's "Friday" LITERAL VERSION)

Don't miss the lyrics XDD

Nothing better to relax than a good laughter with a hilarious film. This has been my best contribution to youtube so far: 23.000 views. It was created in a library 4 years ago an afternoon when my brain was begging for a scape-way...

And finally, I'm glad to post here your last exam grades:

AD01

9,1

BC01

8

AD02

7,7

BC02

6,2

AD03

8,7

BC03

8,4

AD04

9,6

BC04

8,7

AD05

9

BC05

8,9

AD06

8,9

BC06

8,9

AD07

8,7

BC07

7

AD08

6,5

BC08

6,7

AD09

8,9

BC09

10

AD10

8,8

BC10

9,1

AD11

4,3

BC11

9,3

AD12

3,9

BC12

3,8

AD13

8,1

BC13

6,4

AD14

9,5

BC14

8,8

AD15

6,1

BC15

9,7

AD16

9,5

BC16

8,9

AD17

4,5

BC17

8

AD18

6,5

BC18

8,7

AD19

9,4

BC19

7

AD20

8,3

BC20

8

AD21

6,2

BC21

6,5

AD22

7,1

BC22

9,6

AD23

9

BC23

8,7

BC24

8,3

PS: Iñaki, Jorge, Ivan, Carlos, María G, Tania, Veronica and Xabier have given a (more or less) accurate answer to the previous challenge. Rejoice in your deserved new positive! :D

I very much hope you're having a good time during these four days off Spanish tradition have granted to you :P

Next monday is the fifth of November and, thanks to Maria, I remembered that it is Guy Fawkes' day!! Have you ever wondered where do the Anonymous masks come from??

There is an astonishing Comic called "V for Vendetta" which inspired a not less impressive movie 6 years ago. I strongly recommend both of them to you, they're worthy your time!

Now, as far as the last challenge is concerned, I'm glad to write here that Jorge, Iván, Sergio, Juan, Tania and Carlos deserve a new positive. Not all the answers were as precise as I wanted, by they were close enough ;)

I have taken that challenge from one of the most famous action-movies of the 90's: "Die Hard with a Vengance", so I would like Mr. Bruce Willis to explain the solution:

Finally, I do not want to compete with Ivan or Sergio's blog, but I'm afraid this piece of news is more hilarious than anything they have uplaoded so far! XDDDD Haahhaha!! !OMG!! And this man is postulating himself for President of the United States!

I am the one who wonders how this man's thoughts look like... And I may have got an answer:

(excerpt from Mitt Romney's thoughts)

Anyway, take care and have fun!

(Freddie Mercury's "Living on my Own" (1985)

I almost forgot to publish your new challenge!! XD Euler Piruleta services are required again!!

You Vs. The Hourglass

Thank God that
Taconera’s Park hasn’t exploded… We shall always be thankful to Euler Piruleta
and his Gang, who managed to solve the problem…

Nevertheless,
now Euler Piruleta has to face a new situation… Due to the American Elections taking
place this weekend, V from “V of Vendetta” is planning to demolish NavarroVillosladaHigh School.
You may think that this is some good news, but the truth is that his plans
affect you all since his idea is to set a bomb someday next week between 9 AM
and 2 PM.

To deactivate
the rudimentary bomb’s mechanism you should practice with these two hourglasses
to learn who to measure exact periods or time.

C’mon!!! You are
our only hope!!

These two
hourglasses last for 7 minutes (the big one) and 4 minutes.

How can we
measure exactly 9 minutes (nor one
second longer, neither shorter) using those hourglasses?

Tip: try to start both hourglasses at the same
time. What happens after exactly 4 minutes?

Verónica, Carlos, Xabier, Iván, María, Iñaki, Tania have given a valid answer for Romeo's Challenge. Congratulations!! :D These are some of your solutions:

And your brand new challenge is the following:

The Gallons’ Problem

Imagine the
following situation: a bomb is set in Taconera’s Park and you are the only on
capable of dismantling it. Spanish CSI Special AgentEuler Piruleta requires your services and you
find yourself before this bomb…

Only 4 minutes
are left before the bomb explodes and the only way of stopping it is placing a
bottle filed with 4
gallons of water in a balance. You have a 3-gallon and a
5-gallon bottle and a fountain with a continuous stream of water…

How can you get
those 4 gallons
inside one bottle using the 3-gallon and 5-gallon bottles?

Remember: our
future depends on you!!! :D

Dedline: October the 31st! Do not forget to post a comment if you discover the solution ^_^

I almost forgoto about this! Do you remember the Ninja Star I took into class last week? Here's a video with some straightforward guidances to learn how to do it! :D

These two snails are Romeo and Juliet. Juliet has been waiting in her balcony for her lover‘s arrival, but Romeo has just had dinner and he has truly forgotten the number of Juliet’s house. Every square represents one house (64 in all, including Romeo’s and Juliet’s) and the passionate lover will visit every single house one time and one time only before reaching to Juliet. You must try to help him to find his way but be careful… he is only allowed to move upwards, downwards, to the left, to the right and diagonally.

One more thing: You are only entitled to use up to 20 straight lines… it seems our little fellow is not keen at all about turning on corners…

The procedure is the same as always: send me an e-mail with the solution and post a comment to this entry. This challenge's deadline is October the 22th. Ony the first 10 valid solutions will get a positive!! Don't miss the chance!

Tip: The best way to try to solve this is copying the image to gimp, paint or a similar software and draw the lines over it.

Thanks to Maria, I have been thinking about the music groups which were beyond famous when I was your age, so I have decided to post here 4 songs that really made an impact in the life of every teenager boy/girl in the mid 90's.... :P You'll notice how times have changed!! XD

I'm quite overwhelmed by your results... Congratulations! Some of you should be proud of yourselves, others should take care of those silly mistakes you sometimes can't avoid making and, finally, there are people whose main problem is the lack of effort and attention in class... Anyway, it's never too late to improve your qualifications!

AB01

8,1

BC01

8,5

AB02

6,7

BC02

4,5

AB03

9,1

BC03

6,4

AB04

7,8

BC04

9,6

AB05

9,1

BC05

9,3

AB06

8,9

BC06

9,2

AB08

7

BC07

8,4

AB09

6,9

BC08

8,3

AB11

2,5

BC09

10

AB13

8,3

BC10

8,9

AB14

9,7

BC11

7,8

AB15

6,7

BC12

5,9

AB16

9,5

BC13

7,8

AB18

7,7

BC14

9,8

AB19

9,6

BC15

9,5

AB20

7,6

BC16

8,9

AB22

8,3

BC17

5,3

AB23

9,6

BC18

8,1

AD07

8,9

BC19

5,3

AD10

9,4

BC20

7,5

AD12

6,1

BC21

6,9

AD17

6,5

BC22

10

AD21

7,4

BC23

6,8

BC24

8

Challenge 2: An almost infinite Addition First of all, congratulations to Laia, Iván, María G., Verónica, Tania, Andrea I., Carlos, Jorge and Xabier. You have given one of the multiple right answers ^_^ Therefore, you have won a Challenge's Possitive. Mathematics is a
science where not only additions and subtractions are featured… There are so
many different fields in mathematics that they are almost endless (analysis, geometry, algebra, statistics,
topology, games theory…) and, sometimes, the problems we have to face
consist on proving some result we think it’s bound to be true (they are usually called theorems). These demonstrations
are usually tough and long, that’s why they involve huge quantities of time,
effort and study so we don’t become nuts with things like….

Your time has come to prove something!!

a)Prove that $0,\widehat{6}+0,\widehat{3}=1$

b)Try to get the
result of the following product of fractions without multiplying all of them
(which would take ages…): $$\left(1-\frac{1}{2}\right) \cdot \left( 1-\frac{1}{3} \right) \cdot \left( 1- \frac{1}{4} \right) \cdot \left( 1 - \frac{1}{5} \right) \cdots \left( 1 - \frac{1}{999} \right) \cdot \left( 1 - \frac{1}{1000} \right)$$

The guidelines are the following: this time you can either send me the answer to my gmail account (if you want, yo may do it with paper and pen and scan it) or bring it to class in a piece of paper. Only the 14 first answers will receive a positive mark. Deadline: October the 13th. Printable version HERE!!

In two weeks Keane will be playing alive in the Baluarte. I had the chance to attend one of their performances and they sounded really impressive ;)