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My wife Carla and I have gone with our children Darío and Elena to my friends Antonio and Beatriz's house to celebrate their son Francisco's birthday. We really like to play a somewhat unique card game in which when you lose a round, you have to double the money that the rest of the players have in their pocket.
Today something very curious happened and that is that each of us has lost a single round in the same order as the alphabetical order of our names, which happens to start all with different letters, and in the end we have all finished with 1, € 28 in your pocket.
How much money have I earned?
I am the one who has lost the last round, since all our names begin with different letters and the rest of the names go from A to F.
Before starting the game, Antonio had € 4.49 in his pocket; Beatriz had € 2.25; Carla € 1.13; Darío 57 cents, Elena 29 cents, Francisco 15 cents and I 8 cents, so I have won € 1.20..
We can find the initial money of each of the participants with the following formula:
2reverse name order × Number of participants + 1
Antonio: 26 × 7 + 1 = 449 cents
Beatriz: 25 × 7 + 1 = 225 cents
Carla: 24 × 7 + 1 = 113 cents
Darius: 23 × 7 + 1 = 57 cents
Elena: 22 × 7 + 1 = 29 cents
Francisco: 21 × 7 + 1 = 15 cents
Me: 20 × 7 + 1 = 8 cents