## IMO 1974/1

Discussion on International Mathematical Olympiad (IMO)
seemanta001
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### IMO 1974/1

Alice, Betty, and Carol took a series of examinations. There were one grade of $A$, one grade of $B$, and one grade of $C$ for each examination, where $A,B$ and $C$ are different positive integers. The final test scores were:

Alice = $20$
Betty = $10$
Carol = $9$

If Betty placed first in the arithmetic examination, who placed second in the spelling examination?
Last edited by Phlembac Adib Hasan on Sun Jan 10, 2016 5:10 pm, edited 1 time in total.
Reason: Fixed grammatical errors and unintended line-breaks
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### Re: IMO 1974/1

seemanta001 wrote:Alice, Betty, and Carol took the same series of examinations. There were one grade of A, one grade of B, and one grade of C for each examination, where A;B and C are different positive integers. The final test scores were
Alice Betty Carol
$20$ $10$ $9$
If Betty placed first in the arithmetic examination, who placed second in
the spelling examination?
This version is quite ambiguous and not the official statement of IMO 1974-1. Let me add that here:
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).
@Kids from junior category, try it before reading further.
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tanmoy
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Joined: Fri Oct 18, 2013 11:56 pm
Phlembac Adib Hasan wrote: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).