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Omni-MATH / Three players A,B and C play a game with three cards and on each of these 3 cards it is written a positive integer, all 3 numbers are different. A game consists of shuffling the ca…

Problem

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problem

Three players A,BA,B and CC play a game with three cards and on each of these 33 cards it is written a positive integer, all 33 numbers are different. A game consists of shuffling the cards, giving each player a card and each player is attributed a number of points equal to the number written on the card and then they give the cards back. After a number (≥2)(\geq 2) of games we find out that A has 2020 points, BB has 1010 points and CC has 99 points. We also know that in the last game B had the card with the biggest number. Who had in the first game the card with the second value (this means the middle card concerning its value).
Plain-text mathematical notation (without MathML)
Three players A,B and C play a game with three cards and on each of these 3 cards it is written a positive integer, all 3 numbers are different. A game consists of shuffling the cards, giving each player a card and each player is attributed a number of points equal to the number written on the card and then they give the cards back. After a number (≥2) of games we find out that A has 20 points, B has 10 points and C has 9 points. We also know that in the last game B had the card with the biggest number. Who had in the first game the card with the second value (this means the middle card concerning its value).
Original LaTeX notation
Three players $A,B$ and $C$ play a game with three cards and on each of these $3$ cards it is written a positive integer, all $3$ numbers are different. A game consists of shuffling the cards, giving each player a card and each player is attributed a number of points equal to the number written on the card and then they give the cards back. After a number $(\geq 2)$ of games we find out that A has $20$ points, $B$ has $10$ points and $C$ has $9$ points. We also know that in the last game B had the card with the biggest number. Who had in the first game the card with the second value (this means the middle card concerning its value).

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Source and history

task_id
a37ff134-07d9-5642-9c96-77cabdd80736
task_key
test--a37ff134-07d9-5642-9c96-77cabdd80736
task_revision_id
1
config / split
/ test

Official source

initial import