1. Late at night, three wizards met at a crossroads. Each had a magic wand in their hands. A strong wind came, snatched their wands, played with them so much that none of the wizards could distinguish their own wand from another's. The wizards had no choice but to pick up the wands at random. Find the probability that none of the wizards picked up their own magic wand.
Solution. The wizards have six different ways to take the magic wands. In only two of the six scenarios, none of the wizards will take their own wand, since the wizard who takes the wand first can take any of the two wands belonging to the other wizards. The remaining wizards have no choice, as one of their wands is still not taken, and thus he must take the other wand. Therefore, the desired probability is $\frac{2}{6}=\frac{1}{3}$.

Answer: $\frac{1}{3}$