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Lê Anh Duy

15/04/2018 at 10:05
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5) There were 9 cards number 1 to 9. Four people A, B, C, D each collected two of them.

   A said: "The sum of my numbers is 6"

   B said: "The difference between my numbers is 5"

   C said: "The product of my numbers is 18"

   D said: " One of my numbers is twice the other"

What is the number on the remaining card?



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  • ...
    Lê Quốc Trần Anh Coordinator 15/04/2018 at 11:00

    We have: 1 + 5 = 2 + 4 = 6 (there are no 2 number-3 cards)

    => A has (1;5) or (2;4) cards [1]

    B said the difference between two cards is 5

    => B has (1;6), (2;7), (3;8) or (4;9) cards [2]

    We have: 2*9 = 3*6 = 18

    => C has (2;9) or (3;6) cards [3]

    We have: 2 = 2*1; 4 = 2*2; 6 = 2*3; 8 = 2*4

    => D has (1;2), (2;4), (3;6) or (4;8) cards [4]

    If A has (2;4) cards => Unsatisfy

    If A has (2;4) cards -> B has (1;6) or (3;8) cards

     - If B has (1;6) cards => Unsatisfy for C

     - If B has (3;8) cards => Unsatisfy for C, too

    => A has (1;5) cards

    => B has (2;7), (3;8) or (4;9) cards

    - If B has (2;7) cards -> C has (3;6) cards -> D has (4;8) cards -> The number of the remaining card is 9.

    - If B has (3;8) cards -> C has (2;9) cards -> Unsatisfy for D

    - If B has (4;9) cards -> C has (3;6) cards -> Unsatisfy for D

    So the number of the remaining card is 9

    Lê Anh Duy selected this answer.
  • ...
    ¤« 16/04/2018 at 14:04

    We have: 1 + 5 = 2 + 4 = 6 (there are no 2 number-3 cards)

    => A has (1;5) or (2;4) cards [1]

    B said the difference between two cards is 5

    => B has (1;6), (2;7), (3;8) or (4;9) cards [2]

    We have: 2*9 = 3*6 = 18

    => C has (2;9) or (3;6) cards [3]

    We have: 2 = 2*1; 4 = 2*2; 6 = 2*3; 8 = 2*4

    => D has (1;2), (2;4), (3;6) or (4;8) cards [4]

    If A has (2;4) cards => Unsatisfy

    If A has (2;4) cards -> B has (1;6) or (3;8) cards

     - If B has (1;6) cards => Unsatisfy for C

     - If B has (3;8) cards => Unsatisfy for C, too

    => A has (1;5) cards

    => B has (2;7), (3;8) or (4;9) cards

    - If B has (2;7) cards -> C has (3;6) cards -> D has (4;8) cards -> The number of the remaining card is 9.

    - If B has (3;8) cards -> C has (2;9) cards -> Unsatisfy for D

    - If B has (4;9) cards -> C has (3;6) cards -> Unsatisfy for D

    So the number of the remaining card is 9



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