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Guardiola: the last training session


FC Barcelona Badge

Guardiola's last training session as FC Barcelona's coach. They've been training for 2 hours preparing the final of the Spanish Cup, and Pep Guardiola proposes to them the last exercise before going to the changing room.

Guardiola picks up to four players to cross the football field from goal to goal passing the ball one each other without dropping it. The four players must leave the same goal area and arrive to the other one. They have 17 minutes to get everyone to the opposite goal. They only have one ball, which will be carried from one goal to the other one. They can cross the field one by one (kicking softly the ball without dropping it), or by pairs (passing the ball from one to the other one without touching the ground). They can't kick the ball from one area to another, but a player must return with it, touching it the manner described. Evidently, some of the players are more skillful than others in handling the ball, so that when two players go together, they will be always crossing the field at the slower speed

The data are as follows:

Messi: takes 1 minute to cross the field kicking the ball.

Iniesta: takes 2 minutes.

Cesc: takes 5 minutes.

Piqué: takes 10 minutes to cross.

For example, if Messi and Cesc cross together the field by passing each other the ball, it takes 5 minutes. Then the ball can be returned by Cesc, and we'll have 10 minutes elapsed from the beginning. Then Cesc and Piqué cross together... and so on with all of them.


With this data, which strategy should use all the players to cross from one goal area to the other one in just 17 minutes?

It's worth thinking about it for some minutes, before going to the solution area. And I promise there's no cheating.

Go to the second half to discover the solution


The solution is as follows:

1. Messi and Iniesta cross the field at first. It takes a total of 2 minutes.

2. Iniesta returns. 4 minutes are consumed.

3. Now Cesc and Piqué cross the field. It takes them 10 minutes, so that we have a total of 14 minutes.

4. Messi returns with the ball. It takes 1 minute, so we totalize 15 minutes.

5. And finally, Iniesta and Messi return again with the ball. It takes 2 minutes to cross, so we get the total of 17 minutes.

You've probably tried more than once with Cesc and Piqué crossing the field together, but the problem was that afterwards one of them had to return, and the time increases exponentially. The solution was in sight: we must return with one of the two quicker players we have, but that means that we need both of them at the opposite goal. The first player, in order to return with the ball after the first trip, and second one, to return the ball after the two slowest players have crossed the field. In fact, the result is the same if, at first, we cross the field with Messi, and then we use Iniesta for the fourth trip.

This is a perfect example of what is known as 'lateral thinking'. The funny thing is that as soon as you find the solution, you can't understand how you didn't happen it before. And the difficulty is that you are unconsciously 'pushing' to go in one direction, and surprisingly that turns out wrong.

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