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?

## IMO 1974/1

- seemanta001
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### IMO 1974/1

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*

*"Sometimes it's the very people who no one imagines anything of who do the things no one can imagine"*- Phlembac Adib Hasan
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### Re: IMO 1974/1

This version is quite ambiguous and not the official statement of IMO 1974-1. Let me add that here: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?

@Kids from junior category, try it before reading further.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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### Re: IMO 1974/1

A nice problem. Here is my solution: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).

"Questions we can't answer are far better than answers we can't question"