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Math Challenges

Rules: 

At the beginning of each month a Math challenge will come out.

To solve the challenge correctly, you have to:

      • Write the solution with an explanation on a paper with your name and group and left it in the mailbox situated in the hall, before the first day of the following month.
      • Write the reasoned solution in this website (at the bottom of the article).

There will be 3 categories: 

  • Pupils (ESO, Batxillerat and Professional Studies).
  • Teachers and PAS.
  • Web visitors.

Mars challenge

There are exactly three different pairs of positive integers that add to make six:

1 + 5 = 6
2 + 4 = 6
3 + 3 = 6

How many different pairs of positive integers add to make one-thousand?

  • Mars solution:

1000/2=500 pairs

Mars winners:

  •  Pupils: JIsaac B., ;artín R., Andreu L. i Shi Ting L. (1r ESO)
  •  Teachers: Alicia

February challenge

Four boys cut a cake in equal parts as you can see in the first figure. Just before each one takes his piece, a girl arrives. Then, the four boys decide to give her a part of his piece, so that everyone will eat the same amount of cake.

What percentage of their part of cake will they have to give to the girl?

  • February solution:

Each boy has 1/4 of the cake. If each one gives her x, the boys will have (1/4 – x).

As the five will have the same part of the cake: (1/4 – x) · 5 = 1 → = 1/20 = 20%

February winners:

  •  Pupils: Joan A., Martín R. i Isaac B. (1r ESO)
  •  Teachers: David Aínsa

January challenge

  • January solution:

  • January winners:
    •  Pupils: Diana J., Martín R. i Isaac B. (1r ESO)
    •  Teachers: David Aínsa

December challenge

How tall is the table?

  • December solution:
  • December winners:
    •  Pupils:  
    •  Teachers: David A.
    •  Web participants: Edgar G.

November challenge

Núria draws a broken line with the vertices on the sides of the  rectangle, which forms angles of 10 °, 14 °, 33 ° and 26 °, as indicated in the figure:

 

How much does the angle α measure?

  • November solution: The angle measures 11o    
  • November winners:
    •  Pupils: Gaia Joustra (1r Batx) 
    •  Teachers: David Aínsa
    •  Web participants: Edgar G.
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