Sunday 28 November 2010

MATHS PUZZLE # 9 FIRST LEG (Second Year)

(from the 29th of November to the 6th of December)


 JULIA'S FIRST DAY AT SCHOOL
It’s the first day of school for Julia. The teacher, Miss Rivas, has told her students to meet in the playground. She says: “You must all shake hands and introduce yourselves”
If there were 10 students in her class, how many handshakes were there?
You can send your answers to matecampanar@gmail.com


SOLUTION
The first student will shake hands with 9 students, the second student with 8, the third student with 7 and so on. So we have 9+8+7+6+5+4+3+2+1 =45

Or another way to solve the problem:

If there are 10 students, each one will give his/her hand to the other 9 students. That is 10 x 9 =90. However, if we calculate the handshakes this way, we are counting each handshake twice: for example when say B greets C and when C greets B. Thus the number of handshakes is half the calculations made above, therefore (10 x 9)/2=45 

Friday 26 November 2010

EU COMPETITION #4 (First leg of Second Year)

E.U. Competition # 4  (First Leg of Second Year) 

Hi! Thanks for your answers! Here are this fortnight's questions:

1.

a) What do these Shakespeare's plays have in common?... Julius Caesar, Richard III, Hamlet, Macbeth. 

2.

a) In which country is the European Court of Justice sited?

b) Which country refused to join the European Economic Community when it was founded in 1957 but later applied three times before actually being admitted?

3.

a) Borders are not respected by nature. Which European countries  does the Danube run through?

b) Which region of the EU is the first to celebrate the New Year?

c)  Finally try these riddles:

Paella is to Spain as Gulash is to ……………..

The Beatles are to Britain as Kabát are to ………………

Hamburg is to Germany as …………………to the Netherlands.

Courmayeur and Cortina d’Ampezzo are to Italy as …………………  and …………………. are to        Switzerland.

 

And that’s all today. Remember to send your answers  to    iescampanar10@gmail.com             CU in 2 weeks!!    P Ú   

SOLUTION:
1.- There is a ghost in all of them
2.-a)Luxembourg City
     b) Great Britain
3.-a)Germany, Austria, Hungary, Serbia, Bulgaria, Moldova, Slovakia, Croatia, Romania,      Ukraine.
     b)New Caledonia (those islands belong to France)
     c)Hungary
        Czech Republic
        Rotterdam
        Zermatt, St Moritz, Les Diablerets  among many other ski resorts.

Thursday 25 November 2010

Video conference: Food for thought



After so much work and long hours preparing it, the video conference did not achieve our goals but partly. Switzerland had some last-minute technical problems and could not participate. As for the other four countries (Hungary, Germany, Czech Republic and Spain),  at least we managed to make the students communicate with their peers in the other schools. The sound was poor sometimes but, all in all, the students had already worked before the video conference (on the topic of "The way I see my country, the way I see others"). Then they spoke to, watched videos made by and listened to other partner schools students during the session. However, what is probably the most positive achievement, is the fact that now they are really interested in video conferencing and contacting and chatting with their old and new friends. It might be really fantastic if we had the means and the time to video conference regularly!
HUEVOS+2222.jpg (88×88)

Sunday 21 November 2010

MATHS PUZZLE # 8 FIRST LEG (Second Year)

 (from the 22nd to the 29th of November 2010)

 

A SHOE-IN
Four young girls, (Aurora, Benita, Clara and Daniela) are talking.
One of them is wearing moccasins; another is wearing ballet shoes; another sandals and the fourth one is wearing tennis shoes.
The one in the ballet shoes says: ‘I like Aurora a lot but I don’t like Daniela at all’.
The one in the sandals says: ‘I dislike Aurora but Clara is a god friend of mine’.
Finally  Daniela says: ‘I am fond of Aurora and I never wear moccasins’.
WHAT KIND OF SHOES IS EACH GIRL WEARING?

You can send the solution to iescampanar11@gmail.com    or to www.Fernando.Escuin@iescampanar.com

SOLUTION:

Discarding all the impossible squares on a double entrance chart, we see that Benita is necessarily the one wearing the sandals whereas Daniela is wearing the tennis shoes.
It is clear then that Aurora in the one in the moccasins and thus Clara the girl in the ballet shoes.


AURORA
         a



BENITA


          a

CLARA

           a


DANIELA



           a

MOCCASINS
BALLET SH.
SANDALS
TENNIS SH.

Sunday 14 November 2010

MATHS PUZZLE # 7 FIRST LEG (Second Year)

(from the 15th to the 22nd of November 2010) 

SUBJECT-IVE  DECISION
Last Summer four Comenius students called Kovács, Müller, Dvořák and González attended an international school, the Collège Sirondi. Each of them took 2 different subjects. Furthermore:
-Three students chose English.
-There was only one student who did Chemistry.
-Two students chose Mathematics.
-Two students, Sophia and the one called González took History.
-Natálie did not study English.
-Dávid chose Mathematics.
-The student called Dvořák did not do any course which was attended by either Pablo or by the student called Müller.
WHAT IS THE FULL NAME OF EACH STUDENT AND WHICH TWO SUBJECTS DID EACH LEARN? The following chart may help you record the information from the clues.

SOLUTION
Since Natálie was the only one that did not take up English and Dvořák did not do any course attended by either Pablo or Müller, it follows that Natálie and Dvořák were the same person and that she chose at least Maths.
Sophia and González did History and were among the three students who learnt English. Natálie Dvořák therefore did Maths and Chemistry.
Because Dávid was also a Maths student, he could not be  González so both Sophia and Pablo studied English and History.
As Sophia and González were two different students, it is clear that Pablo’s surname was González and Sophie´s was Müller, our fourth student being thus Dávid Kovács.
SO

Natálie
Dvořák
Maths
Chemistry
Pablo
González
English
History
Sophia
Müller
English
History
Dávid
Kovács
English
Maths


Saturday 13 November 2010

EU COMPETITION (First leg of Second Year)

E.U. Competition # 3 (First Leg of Second Year) 333333333333333333333333333333

Here are this fortnight's questions:

1.-If PRAG is for Prague and LUG for Lugano, which THREE locations have the following 3-letter codes: MAD, BUD, HAM?
2.-Now for THREE dogs and THREE horses. Whose dogs were these:  ARGOS, SNOWY, GROMIT? Whose horses were these: BUCEPHALUS, BABIECA, MARENGO? 
3.-I would finally like to invite you to visit a most interesting website  where you can see maps and actually read amazing old books and documents. Are you ready?   www.wdl.org/en/browse/item_type.html     Just tell me  in which language THREE of the following documents/books  were written? Just THREE of them!
                 Epic poem 'Parzival'
                 Columbus manuscript
                 'A Book Concerning the Nature of Things'
                 'Selected Fables for Children by La Fontaine'
                 'Declaration of Independence of the United States'
                 'Winds of the Four Directions'
                 'Manifesto to the Czechoslovak People in America'
                 'The Bible of Johannes Gutenberg'
                 'Journal of Magellan's Voyage'
                 'Codex Gigas'
I'll be with you again in two weeks! And be good! Remember that you can send your answers to iescampanar10@gmail.com  
SOLUTION:

  1. MAD=Madrid   BUD= Budapest    HAM=Hamburg
  1. Argos:In Homer's the Odyssey, Argos is Odysseus' faithful dog.Snowy:Snowy(French: Milou) is an Adventures of Tintin characters. He is a white Wire Fox Terrier. Gromit:Wallace and Gromitare the main characters in a series consisting of four British animated short films and a feature-length film by Nick Park of Aardman Animations.  All the characters are made from moulded plasticine modelling clay on metal armatures, and filmed with stop motion clay animation.
Bucephalus:Bucephalusor Bucephalas was Alexander the Great's horse and one of the most famous actual horses of antiquity.
Babieca:Babieca is one of the most famous horses in history. As El Cid's charger the story of his life has become surrounded in myth and legendwith the passage of time.
Marengo:Marengo(c. 1793 - 1831) was the famous war mount of Napoleon I of France. Named after the Battle of Marengo, through which he carried his rider safely, Marengo was imported to France in 1799 as a 6-year-old.
  1. Epic poem ‘Parzival’: Middle High German; Columbus manuscript: Spanish; Winds of the Four Directions: Chinese; Fables of La Fontaine in French; Codex Gigas in Latin; The Bible of Gutemberg in Latin; Magellan's Voyage in French; the Manifesto in Czech; The Declaration of Independence in English; the Book Concerning the Nature of things in Latin.

Sunday 7 November 2010

MATHS PUZZLE # 6 FIRST LEG (Second Year)

(from the 8th to the 15th of November 2010)

THE GIFT

A group of friends decided to buy a present whose price is a number between 175 and 195 euros. In the last moment two friends decided not to participate, so the rest of the group had to pay one more euro. Which is the price of the present if we know it is an integer?

You can send the solution to www.Fernando.Escuin@iescampanar.com

SOLUTION
For factorial decomposition of the numbers between 170 and 195 only 180 is a product of two different forms xy = (x-2) (y + 1) (180 = 20 x 9 = 18 x 10). So 180 is the solution.
Where x = number of friends and y = euros by person.
In a different way,
We have the following equations system:
P= xy and P= (x -2) ( y+ 1) → xy = xy + x – 2y – 2 → x = 2 + 2y
xy = P → (2 + 2y ) y = P → 2 y2 + 2y – P = 0
Where P is the cost of the gift.
The discriminant of this second grade equation Δ = 4 + 8P has to a rational number. This is possible if P=180 → Δ = 38 → y = (-2 + 38 )/4 = 9 and x = 180/9 = 20.



Thursday 4 November 2010

THE SWISS TEAM READY TO TRAVEL TO LÜNEBURG

Students Yohann Monneau, Sinéad Lynch, Cécile Walder, Morgane Taddeo and Amiel Guyot are posing in the photo flanked by their teachers Stéphane Garcia (left) and Olivier Dubois (right). They form the team that will represent their school -Collège Sismondi in Geneva, in the project forthcoming visit to Lüneburg, Germany.

Monday 1 November 2010

MATHS PUZZLE # 5 FIRST LEG (Second Year)

(from the 1st to the 8th of November)

The digit on the left of a six-digit number is 1. Moving this 1 to the other extreme, the number is three times higher than the first number.

What is the original number?

You can send the solution to FernandoEscuin@iescampanar.com 


SOLUTION

 

1abcde x  3 = abcde1   ð    3e finishes  in 1       ð    e = 7

1abcd7 x 3 = abcd71    ð    3d+2 finishes in 7    ð    3d finishes in 5   ð  d=5
1abc57 x 3 = abc571    ð    3c + 1 finishes in 5  ð    3c finishes in 4   ð  c=8
1ab857 x 3 = ab6571   ð    3b+2 finishes in 8    ð    3b finishes in 6   ð  b=2
1a2857 x 3 = a28571   ð    3a finishes in   2      ð    a = 4

The number is 142857

SOLVED IN A DIFFERENT FORM:
3(100.000 + x ) = 10x +1
300.000 + 3x = 10x + 1
299.999 = 7x
x = 42857
The number is 142857