Figuri geometrice / Geometric Figures (dificultate:10%) - termen limita 27.08.2017

Ovidiu a fost incantat de jocul primit – jocul de domino, propus de Radu si cumparat de Petru in aceasta dimineata.

Petrecerea de la birou se finalizeaza, insa Ovidiu le propune prietenilor sa continue la o bere intr-unul din barurile din apropiere. Vor merge la barul din colt, cunoscut pentru atmosfera interesanta intretinuta de jocurile disponibile pentru clienti si meciurile de fotbal.

 

A. Figuri Geometrice

Colegii isi amintesc ca ultima data cand au fost in acest bar, au gasit un joc interesant. Acesta continea poligone regulate, toate diferite ca forma si marime. Jocul cerea sa se intalneasca intr-un punct varfurile a cinci astfel de poligoane, asezate in acelasi plan si fara a se suprapune deloc unul peste altul. Ce poligoane au ales? 

Sursa: Nicolae Oprisiu, Olimpiada jocurilor rationale, Ed, Dacia, 1984

 

Ovidiu was happy with his present - the domino game, a proposal of Radu bought this morning by Petru.

The party ends at the office, but Ovidiu proposes to his friends to go out for a beer in one of the nearby bars. They will go to the bar on the corner, which is known for the nice atmosphere due to board games and football matches.

 

A. Geometric Figures

Everybody remembers that the last time they have been to this bar, they found an interesting game. It contained regular polygons, all different in shape and size. The game required to meet the peaks of five such polynomials in one point such that the polygons are in the same plane without overlapping each other. What polygons did they choose?

Source: Nicolae Oprisiu, Olimpiada jocurilor rationale, Ed, Dacia, 1984


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szabozoltan

Corect: Ce poligoane a ales? (în loc de polinoame - a se vedea şi în textul englezesc)


Denumire / Name (dificultate:5%) - termen limita 27.08.2017

Petrecaretii ajung in bar. Se aseaza la masa, comanda o bere si primesc o informatie: se cauta un nume pentru un nou sortiment de bere.

 

B. Denumire

Pentru ca numele interesante atrag clienti interesanti, se doreste un cuvant cat mai lung, din care prin eliminarea pe rand a cate unei sigure litere sa se formeze de fiecare data un alt cuvant valid, pana cand ramane o singura litera.

Spre exemplu:

a) pornind de la cuvantul MARE, se pot elimina M, A si in final R, obtinand:

MARE => ARE => RE => E.

b) pornind de la cuvantul AUR, se pot elimina R, apoi U:

AUR => AU => R.

Toate cuvintele obtinute sunt valide, cu inteles in limba romana.

Fiecare litera a cuvantului valoreaza 0.5 pct., cu un maxim posibil de 5 pct. (chiar daca sunt cuvinte mai lungi de 10 litere care satisfac cerintele, se vor puncta cu 5 pct.). Astfel MARE corespunde unul punctaj de 2 pct. si AUR de 1,5 pct.

Nota: Se considera literele fata diacritice.

Sursa: problema originală (Ruxandra F. Olimid)

 

They arrive at the bar, sit down at the table, order a beer and find an iformation: a name for a new assortment of beer is being sought.

 

B. Name

Because interesting names attract interesting clients, they are looking for a long word such that removing one letter at a time (until there is only one letter left) a new valid word is obtained.

For example, starting from the word SONG, G, N, respectively O can be eliminated:

SONG => SON => SO => S.

All intermediary words are valid, with a meaning in English.

Each letter is 0.5 points, and the maximum is 5 points. (Words with more than 10 letters will be assigned 5 points.). So, SONG is 2 points.

Source: original problem (Ruxandra F. Olimid)


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szabozoltan

1. Literele se pot elimina doar de la margini?

2. Literele rămase se pot interschimba între ele?


ruxandra

Literele se pot elimina atat de la margini cat si din interiorul cuvantului, insa ordinea literelor in cuvant nu se poate schimba. 


Fotbal / Football (dificultate:10%) - termen limita 27.08.2017

Consumatia este gratuita pentru masa care propune cel mai lung cuvant, asa ca echipa se pune pe treaba.

Dar sesiunea de brain storming este in curand intrerupta de inceperea meciului de fotbal.

 

C. Fotbal

Joaca una dintre echipele favorite ale lui Petru. Sunt 7 jucatori cunoscuti. Fiecare ocupa o pozitie diferita, un alt numar pe tricou si o alta inaltime. Puteti afla pentru fiecare ce pozitie ocupa, care este numarul de pe tricou si ce inaltime are?

1. Jan este portar

2. Dreapta-fata este nr.10

3. Portarul are 1,72m

4. Jenica are 1,64m

5. Rica joaca dreapta-fata

6. Jucatorul de langa Rica este nr.14

7. Jucatorul care are 1,72 este nr.16

8. Nr.10 are 1,67m

9. In stanga-fata este nr.15

10. Bogdan este in spate-dreapta

11. Banu este nr.20

12. Mihai are 1,80m

13. Mircea poarta nr.6

14. Mihai joaca pe pozitia stanga-fata

15. Nr.42 este dreapta-spate

16. Bogdan are 1,57m

17. Nr.6 este centru-spate

18. Nr.15 are 1,80m

19. Nr.20 are 1,70m

20. Mircea are 1,69m

21. Nr.14 are 1,64m

22. Jucatorul cu inaltimea de 1,70m joaca in stanga-spate

23. Jenica joaca in centru-fata.

Sursa: adaptare dupa o problema de pe Math is Fun - https://www.mathsisfun.com/

 

Consumption is free for the table that proposes the longest word, so the team starts to think.

But the brain storming session is soon interrupted by the start of the soccer match.

 

C. Football

One of Petru's favorite teams is playing. There are 7 popular players. Each of them occupies a different position, wears another T-shirt number and has another height. Can you find out for everyone what position he plays on, what is the number on his T-shirt and what is his height?

1. Jan is the goalkeeper

2. Right-front is No.10

3. The goalkeeper is 1.72m

4. Jenica is 1.64m

5. Rica plays right-front

6. The player next to Rica is No.14

7. No.16 is 1.72

8. No.10 is 1.67m

9. The left-front side is No.15

10. Bogdan is right-back

11. Banu is No.20

12. Mihai is 1.80m

13. Mircea wears No.6

14. Mihai plays in the left-front position

15. No.42 is right-back

16. Bogdan is 1.57m

17. No.6 is the center-back

18. No.15 is 1.80m

19. No.20 has 1.70m

20. Mircea is 1.69m

21. No.14 is 1.64m

22. The player that is 1.70m plays left-back

23. Jenica plays center-front.

Source: adaptation from Math is fun - https://www.mathsisfun.com/


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