At the Beijing Olympics, Maria and Tânia, who are women, and Juan and David, who are men, sat at a square table, as indicated below. All are athletes and each of them practices a different sport: swimming, volleyball, gymnastics, and athletics.

(a) The one who practices swimming was to the left of Maria.

(b) The one who practices gymnastics was opposite Juan.

(c) Tânia and David sat next to each other.

(d) A woman sat next to the one who practices volleyball.

Which of the athletes practices athletics?
To start, we choose a place for one of the athletes, let's say, for Maria.

![](https://cdn.mathpix.com/cropped/2024_05_01_666a1aec7e447b0a6cbeg-093.jpg?height=172&width=263&top_left_y=2344&top_left_x=928)
(a) The person who practices swimming is to the left of Maria. Therefore, we can only have the configuration below.

![](https://cdn.mathpix.com/cropped/2024_05_01_666a1aec7e447b0a6cbeg-094.jpg?height=208&width=263&top_left_y=433&top_left_x=1022)

(b) The person who practices gymnastics is in front of Juan. There are two unique possibilities: Maria practices gymnastics or Maria does not practice gymnastics.

Maria practices gymnastics

![](https://cdn.mathpix.com/cropped/2024_05_01_666a1aec7e447b0a6cbeg-094.jpg?height=257&width=420&top_left_y=928&top_left_x=447)

Maria does not practice gymnastics

![](https://cdn.mathpix.com/cropped/2024_05_01_666a1aec7e447b0a6cbeg-094.jpg?height=285&width=289&top_left_y=914&top_left_x=1546)

(c) Since Tânia and David sat together, only the second option from the previous item - Maria does not practice gymnastics - can satisfy this condition. This generates the following two possibilities.

Maria does not practice gymnastics

![](https://cdn.mathpix.com/cropped/2024_05_01_666a1aec7e447b0a6cbeg-094.jpg?height=320&width=394&top_left_y=1482&top_left_x=431)

Maria does not practice gymnastics

![](https://cdn.mathpix.com/cropped/2024_05_01_666a1aec7e447b0a6cbeg-094.jpg?height=320&width=374&top_left_y=1479&top_left_x=1458)

(d) Since a woman sat next to the person who practices volleyball, it is the second option above that is correct, and we have two possibilities for the athlete who practices athletics: David or Maria.
![](https://cdn.mathpix.com/cropped/2024_05_01_666a1aec7e447b0a6cbeg-094.jpg?height=320&width=1478&top_left_y=2076&top_left_x=401)

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