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Math Help - Basketball Cards....

  1. #1
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    Unhappy Basketball Cards....

    Need some help with this.... Very confused...

    I have a card with a value of 5 and 5 cards with a value of 10. I wish to trade my cardswith a guy for a complete set (1 to 10). However, he has some rules.
    - you give him 2 cards and ask for 3 which add up to the same value as your 2 (eg. you give him 8 and 6 and ask for 7, a 4 and a 3 or two 5's and a 4.)

    - you cannot ask for a card with a higher value than the best one you gave him (eg. he won't trade your two 9's for a 10,6 and 2)

    - He never does a two for one swap (eg. if you give him a 9, he won't give you a 7 and a 2 - this is not gonna happen)

    - You can't sacm him either, by trying to give him a 9 and a 6 for a 7, a 6 and a 2.

    Somehow, I managed to get acomplete set thorugh trading alone.

    a) Explain why I could not have done this if i had only four 10's, a 9 and a 5 to start with.

    b) How many times did I trade with the guy (with five 10's and a 5) to get my complete set?

    c) Show how I might have completetd my set (write down the different steps)

    d) Another person who wishes to trade has two 10's, three 9's and an 8. Show how he could have completed his set.(write down the different steps)

    Hope someone can help.....
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  2. #2
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    Quote Originally Posted by moshiman
    Need some help with this.... Very confused...

    I have a card with a value of 5 and 5 cards with a value of 10. I wish to trade my cardswith a guy for a complete set (1 to 10). However, he has some rules.
    - you give him 2 cards and ask for 3 which add up to the same value as your 2 (eg. you give him 8 and 6 and ask for 7, a 4 and a 3 or two 5's and a 4.)

    - you cannot ask for a card with a higher value than the best one you gave him (eg. he won't trade your two 9's for a 10,6 and 2)

    - He never does a two for one swap (eg. if you give him a 9, he won't give you a 7 and a 2 - this is not gonna happen)

    - You can't sacm him either, by trying to give him a 9 and a 6 for a 7, a 6 and a 2.

    Somehow, I managed to get acomplete set thorugh trading alone.

    a) Explain why I could not have done this if i had only four 10's, a 9 and a 5 to start with.
    After a trade the total value of your cards is the same as before.

    The value of a complete set is 55.

    If you have 4x10, 1x9, and 1x5 initially your initial total is 54, therefore
    as your total is conserved in a trade you can never make a complete set.

    RonL
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  3. #3
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    Quote Originally Posted by moshiman

    b) How many times did I trade with the guy (with five 10's and a 5) to get my complete set?
    On each trade you increase the number of cards you hold by 1.

    You start with 5 cards and end with 10, so you made 5 trades.

    Ooops, you start with six cards and end with 10, so that's 4 trades.

    RonL
    Last edited by CaptainBlack; June 11th 2006 at 03:52 AM.
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  4. #4
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    Quote Originally Posted by moshiman
    c) Show how I might have completetd my set (write down the different steps)
    start with:
    10 10 10 10 10 5 trade 10 5 for 6 5 4
    10 10 10 10 6 5 4 trade 10 5 for 7 5 3
    :
    :
    and so on

    RonL
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  5. #5
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    Talking Thanks

    Thank you all for your help!
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  6. #6
    Newbie carlochick's Avatar
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    Unhappy

    Quote Originally Posted by CaptainBlack
    start with:
    10 10 10 10 10 5 trade 10 5 for 6 5 4
    10 10 10 10 6 5 4 trade 10 5 for 7 5 3
    :
    :
    and so on

    RonL
    but that is breaking the last rule! :
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  7. #7
    Newbie carlochick's Avatar
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    Question Urgent!!!!!!!!!!!!!!!!!!!!

    Need some help with this.... Very confused...

    I have a card with a value of 5 and 5 cards with a value of 10. I wish to trade my cardswith a guy for a complete set (1 to 10). However, he has some rules.
    - you give him 2 cards and ask for 3 which add up to the same value as your 2 (eg. you give him 8 and 6 and ask for 7, a 4 and a 3 or two 5's and a 4.)

    - you cannot ask for a card with a higher value than the best one you gave him (eg. he won't trade your two 9's for a 10,6 and 2)

    - He never does a two for one swap (eg. if you give him a 9, he won't give you a 7 and a 2 - this is not gonna happen)

    - You can't sacm him either, by trying to give him a 9 and a 6 for a 7, a 6 and a 2.

    Somehow, I managed to get acomplete set thorugh trading alone.

    a) Explain why I could not have done this if i had only four 10's, a 9 and a 5 to start with.

    b) How many times did I trade with the guy (with five 10's and a 5) to get my complete set?

    c) Show how I might have completetd my set (write down the different steps)

    d) Another person who wishes to trade has two 10's, three 9's and an 8. Show how he could have completed his set.(write down the different steps)

    Hope someone can help.....
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  8. #8
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    Quote Originally Posted by carlochick
    but that is breaking the last rule! :
    Which rule is trading a 10 and a 5 for a 7, 5, and a 3 breaking?

    RonL
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  9. #9
    Newbie carlochick's Avatar
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    you can't scam him either, by trying to give him a 9 and a 6 for a 7,6 and a 2
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  10. #10
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    Quote Originally Posted by carlochick
    you can't scam him either, by trying to give him a 9 and a 6 for a 7,6 and a 2
    Well that does make it more complicated

    RonL
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  11. #11
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    For (a) simply note that the total value of your cards remains unchanged by each transaction. Since 1+2+...+10 = 55 you need to start off with a total of 55. If you had 4 10's, a 9 and a 5 that would only add up to 54.

    For (b) note that each transaction increases the number of your cards by exactly one. To get from 6 cards to 10 you must make just 4 transactions.
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  12. #12
    Newbie carlochick's Avatar
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    Exclamation

    can you tell me anything on c and d?

    ASAP
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  13. #13
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    Try this for (c)

    Start with 10,10,10,10,10,5

    10+10 -> 8+7+5 giving 10,10,10,8,7,5,5
    10+5 -> 8+6+1 giving 10,10,8,8,7,6,5,1
    10+5 -> 9+3+3 giving 10,9,8,8,7,6,3,3,1
    8+3 -> 5+4+2 giving 10,9,8,7,6,5,4,3,2,1
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  14. #14
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    oh ya... didn't notice that till carlochick brought that up. captainblack,according to this two rules,

    - He never does a two for one swap (eg. if you give him a 9, he won't give you a 7 and a 2 - this is not gonna happen)

    - You can't sacm him either, by trying to give him a 9 and a 6 for a 7, a 6 and a 2.

    i dun think this step would be acceptable :

    10 10 10 10 10 5 trade 10 5 for 6 5 4

    so is there any other answers for this question? i tried doing what captainblack said but i end up failing the last rule...
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  15. #15
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    Thumbs up Thx everyone

    thx everyone for all ur help. finally completed the question. thx again.
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