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!