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Math Help - Counting problem

  1. #1
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    Counting problem

    Hi,
    I have a problem with this exercise - How many ways are there of putting 15 pennies into three piles (each with at least one penny) such that each pile contains an odd number of pennies? I think that the answer is seven, but have difficulties to write it down in a formal way. I would be greateful for any help.
    Thanks in advance...
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  2. #2
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    If the ‘piles’ are unordered then the answer is clearly seven. A simple listing will show that. I do think that is what the problem means.

    However, if the ‘piles’ are ordered then the answer is twenty-eight. I don’t think that is what is meant.
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  3. #3
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    Hello, Gibo!

    I agree completely with Plato's explanation.


    \text{How many ways are there of putting 15 pennies into 3 piles}
    \text{(each with at least one penny) such that each pile contains}
    \text{an odd number of pennies?}

    I tried to find a more formal approach to this problem,
    . . but ended up Listing the cases anyway.


    Place one penny in each pile: . |\;\circ\;|\;\circ\;|\;\circ \;|

    Form the other 12 pennies into pairs:. (\circ\:\circ)\;(\circ\:\circ)\;(\circ\:\circ) \;(\circ\:\circ)\;(\circ\:\circ)\;(\circ\:\circ)


    Now distribute the pairs among the three piles. .There are seven ways:

    . . [0,0,6],\;[0,1,5],\;[0,2,4],\;[0,3,3],\;[1,1,4],\;[1,2,3],\;[2,2,2]

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  4. #4
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    Thanks a lot for help
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