Opinion – Marcelo Viana: Puzzles to end 2022

It is a tradition for this column to end the year with an invitation to readers to have fun with math and logic challenges as a family. Hope you like it!

1. Ada and Bia like to play tennis, betting R$ 1 on each game. Ada won three bets, but ended up losing five reais. How many games did they play?

2. On a trip, Malba Tahan comes across a fork in the road: in one direction, is Mentirópolis, where everyone lies all the time; in the other is Truelandland, where everyone always tells the truth. Next to the fork is a resident of one of the two cities, but we don’t know which one. What question should Malba Tahan ask this person to find the way to Truelandland?

3. Every day, a ship leaves Rio de Janeiro for Lisbon and, at the same time, another ship leaves in the opposite direction, from Lisbon to Rio de Janeiro. I am on one of these ships, returning to Brazil, and I know that the trip lasts exactly 12 days and 12 nights in each direction. How many times, during the voyage, will my ship cross paths at sea with others going in the opposite direction?

4. Three cowboys are in a row. Ado, the tallest, is behind and sees the other two. Caio, the youngest, is in front and, therefore, does not see anyone. Beto is in the middle and only sees Caio. The three are close and listen to each other. While they were blindfolded, hats were placed on their heads. They know that there were three black and two white hats, but the remaining hats were taken from the premises before their blindfolds were removed. Asked, Ado replies that he doesn’t know the color of his own hat. Then Beto informs him that he doesn’t know the color of his hat either. Finally, Caio announces happily that he does know the color of his hat. What is the color, and how did he know?

5. On a circular table are seven lighted magic candles. Each time a candle is blown out, both it and the two neighbors go out. But if we blow out a candle that is out, it lights up again, and the same happens to neighboring ones that are out. In fact, whenever a candle is blown out, both it and the two neighboring candles change state—from lit to unlit, or from unlit to lit. How to blow out all seven candles at the same time?

Answers are welcome by email [email protected].

Happy New Year wishes to everyone!