**Versión española:**

**Contrarreloj ciclista**

**2012 European Championship**, the Spanish team is practicing

**penalty**shots.

The assitants pick all the

**balls**and put them into a**basket**beside the penalty spot.**Xabi Alonso**is the first to train his shots, and he uses

**half**of the balls in the basket

**plus one ball more**.

**Fernando Torres**goes in second place, and he also uses half of the remaining balls into the basket, plus one ball more.

Afterwards,

**Cesc**tries kicking, and he uses half of the reamining balls plus one.
Then,

**Iniesta**does the same, and he also uses one half of the balls in the basket plus one.
Finally it's up to

**Sergio Ramos**, but he can not kick any ball as there's**no ball**in the basket.
How many balls where there in the beginning?

To solve it the best possible way, we start counting from the last player to kick.

We know that

**Sergio Ramos**found no ball in the basket, so**Iniesta**necessarily kicked 2 balls. That way he took half of the balls (2/2=1) plus 1.
We can calculate it as follows: we take the balls he leaves in the basket
(0), we add 1, and multiply the result by two:

(0+1)

**·**2 = 2
When

**Fabregas**takes half the balls remaining in the basket there must be the 2 balls Iniesta kicked later and the balls**Cesc**used. That is, there were 6 balls: he took half the balls (6/2=3) plus 1, and left the 2 balls**Iniesta**kicked. We can calculate it as in the previous case:
(2+1)

**·**2 = 6
Following the same scheme,

**Fernando Torres**will find 14 balls: he picks half of them (7) plus one, and leaves 6 to**Cesc**. If we calculate backwards:
(6+1)

**·**2 = 14
And finally we come to

**Xabi Alonso**. Following the reasoning, he will initially have:
(14+1)

**·**2 = 30 ballsAnd this is the correct answer. In the beginning, we got 30 balls in the basket!

## No comments:

## Post a Comment