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Devious High School had a newly formed chess team that played against all the other high schools in the area this year. These matches are played with a 5-player team who, at a match, sit next to each other on one side of a long table, with the opposing team seated on the other side. It's customary to put your best player on Board 1 and worst on Board 5. At a match, Board 1 players do "hide-the-pawn" to see who plays White, and the other boards alternate colors, so at any match, Devious is playing White either on Boards 1, 3, and 5 or on Boards 2 and 4. Each board has its own chess clock, which operates as any chess clock in a tournament. There are 10 matches in a season.

Devious just happens to have the state's best player, Maria, who won the state title last year. Let's assume she was guaranteed to win every game she played. Unfortunately, the four other players were true novices, who barely knew the rules of chess and how the clocks worked. There was an excellent chance all of them would lose any one match.

Chess Coach Sly came up with a plan. And at the end of the season Devious High School was on top with a 10-0 record—undefeated!

Knowing:

  1. Devious broke no rules of chess whatsoever during any match. No earpieces, cameras, spectator gestures, electronics, etc. No chicanery with the pieces or the clocks. The five Devious players did not communicate with each other in any way during the games.

  2. Matches were played as outlined above. No game or match was interrupted.

  3. Maria did, in fact, win all her games, as was all but guaranteed.

  4. This is not a "trick question" where the explanation is a joke or play on words. The five Devious players just sat down and played their respective matches.

Problem:

  1. What was the plan Devious came up with that allowed it to win all all ten matches?

  2. What was the final score of every match? (Your team gets 1 point for each win at a board; none for each loss; and 1/2 point for each draw. So your team score for a match can range from 5-0 to 0-5 by half-points.)

Hint 1

An intimate knowledge of the game of chess and its strategy is not essential to solving this problem.

Hint 2

The final score was the same in all ten matches.

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    $\begingroup$ What is your definition of "communicate?" technically one could construe copying another player's move as a form of communication because communication is simply "the intentional transfer of information from one person to another." $\endgroup$
    – Ankit
    Commented Aug 9, 2021 at 17:12
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    $\begingroup$ If I paint my house the same color as your house it may or may not be because we communicated. And if we didn't, how can you infer my intention. Are my colors limited to any color except those of houses x, y, z.... if there is no rule? $\endgroup$
    – DjinTonic
    Commented Aug 9, 2021 at 18:18
  • $\begingroup$ And to add to that, since the Devious players are copying from the opponent of the other board, and not copying their teammates, they are not communicating with each other. $\endgroup$
    – justhalf
    Commented Aug 9, 2021 at 18:39
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    $\begingroup$ @justhalf I agree -- edited. $\endgroup$
    – DjinTonic
    Commented Aug 9, 2021 at 18:46
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    $\begingroup$ Time trouble is very common in chess, In practice, copying a straight 40 half games without ever falling victim to it strikes me as rather unlikely. $\endgroup$
    – loopy walt
    Commented Aug 9, 2021 at 20:19

1 Answer 1

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I think the answer is as follows

Given that Maria would win all her matches then the other four players just needed to achieve an overall score of 2-2 in their matches to ensure a 3-2 win for Devious High School in each competition.

They can achieve this by pairing up the players on Boards 2 and 3 and also pairing the players on Boards 4 and 5. Then each player just copies the moves of the opponent on the paired board. For example, if Devious play white on Board 2 and black on Board 3 then the player on Board 2 copies the moves made by white on Board 3 and the player on Board 3 copies the moves made by black on Board 2. Thus you have two copies of the same game and Devious is guaranteed to either have one win or two draws on each pair of boards.

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  • $\begingroup$ but wouldn't the teams catch up to this strategy once the players compare their games? Especially since they sit right next to each other? $\endgroup$
    – Sid
    Commented Aug 9, 2021 at 17:15
  • $\begingroup$ Are the players close enough to see each other's boards? I would think that they would be separated more for a competition, no? $\endgroup$
    – bobble
    Commented Aug 9, 2021 at 17:17
  • $\begingroup$ @bobble the problem says that they all sit at the same table. in order not to be able to see the board they would probably have to be spaced out 10 ft. I don't think these schools would be using 40 ft tables! $\endgroup$
    – Ankit
    Commented Aug 9, 2021 at 17:22
  • $\begingroup$ In real team competition, players are seated next to each other and can easily watch the other games. The real risk with this strategy is not making the moves as fast as the person you are copying and losing on time. But because teams can and do watch each other's games, I don't understand the part about the opponents not catching on $\endgroup$
    – SteveV
    Commented Aug 9, 2021 at 18:10
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    $\begingroup$ Some interesting discussion of this over here. $\endgroup$
    – SteveV
    Commented Aug 9, 2021 at 20:04

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