Question 124
The magician Magimático calls three people from the audience, Ana, Beto and Caio, to help with his math magic. He tells each of them to think of a number from 1 to 50, without revealing it to the magician, and to tell it to each of the other two participants. Then each of them must simultaneously replace their number by the sum of the numbers of the other two. For example, Ana now has the sum of the numbers of Beto and Caio. Magimático then asks them to repeat this process once more. After the second exchange is finished, he asks them to say their numbers. Ana answers 104, Beto 123 and Caio 137. To everyone's surprise, Magimático guesses the numbers initially chosen by the three. What were the numbers initially chosen?