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Math Help - math league

  1. #1
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    math league

    Of the integers between 10^3 and 10^4 that have no repeated digit, how many have digits that increase from left to right?
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  2. #2
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    Re: math league

    Quote Originally Posted by victorwen28 View Post
    Of the integers between 10^3 and 10^4 that have no repeated digit, how many have digits that increase from left to right?
    Any subset of four nonzero digits fits that description.
    So \binom{9}{4}=~?
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  3. #3
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    Cool Re: math league

    126

    {1234, 1235, 1236, 1237, 1238, 1239, 1245, 1246, 1247, 1248, 1249, 1256, 1257, 1258, 1259, 1267, 1268, 1269, 1278, 1279, 1289, 1345, 1346, 1347, 1348, 1349, 1356, 1357, 1358, 1359, 1367, 1368, 1369, 1378, 1379, 1389, 1456, 1457, 1458, 1459, 1467, 1468, 1469, 1478, 1479, 1489, 1567, 1568, 1569, 1578, 1579, 1589, 1678, 1679, 1689, 1789, 2345, 2346, 2347, 2348, 2349, 2356, 2357, 2358, 2359, 2367, 2368, 2369, 2378, 2379, 2389, 2456, 2457, 2458, 2459, 2467, 2468, 2469, 2478, 2479, 2489, 2567, 2568, 2569, 2578, 2579, 2589, 2678, 2679, 2689, 2789, 3456, 3457, 3458, 3459, 3467, 3468, 3469, 3478, 3479, 3489, 3567, 3568, 3569, 3578, 3579, 3589, 3678, 3679, 3689, 3789, 4567, 4568, 4569, 4578, 4579, 4589, 4678, 4679, 4689, 4789, 5678, 5679, 5689, 5789, 6789}
    Last edited by MaxJasper; October 14th 2012 at 03:36 PM.
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  4. #4
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    Re: math league

    But there is a condition that the digits that have to increase from left to right.
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  5. #5
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    Re: math league

    Is there a way to do it without listing all the possibilities?
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  6. #6
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    Re: math league

    Quote Originally Posted by MaxJasper View Post
    126
    {1234, 1235, 1236, 1237, 1238, 1239, 1245, 1246, 1247, 1248, 1249, 1256, 1257, 1258, 1259, 1267, 1268, 1269, 1278, 1279, 1289, 1345, 1346, 1347, 1348, 1349, 1356, 1357, 1358, 1359, 1367, 1368, 1369, 1378, 1379, 1389, 1456, 1457, 1458, 1459, 1467, 1468, 1469, 1478, 1479, 1489, 1567, 1568, 1569, 1578, 1579, 1589, 1678, 1679, 1689, 1789, 2345, 2346, 2347, 2348, 2349, 2356, 2357, 2358, 2359, 2367, 2368, 2369, 2378, 2379, 2389, 2456, 2457, 2458, 2459, 2467, 2468, 2469, 2478, 2479, 2489, 2567, 2568, 2569, 2578, 2579, 2589, 2678, 2679, 2689, 2789, 3456, 3457, 3458, 3459, 3467, 3468, 3469, 3478, 3479, 3489, 3567, 3568, 3569, 3578, 3579, 3589, 3678, 3679, 3689, 3789, 4567, 4568, 4569, 4578, 4579, 4589, 4678, 4679, 4689, 4789, 5678, 5679, 5689, 5789, 6789}
    What a useless reply.

    Quote Originally Posted by victorwen28 View Post
    But there is a condition that the digits that have to increase from left to right.
    Example: Consider the set \{2,4,1,6\}, how many ways can you arrange that set into a four-digit number of increasing digits, (in the literature that is known as a strictly sorted integer).
    So there is an one-to-one correspondent between the strictly sorted four digit integers and the four elements subsets of \{1,2,3,4,5,6,7,8,9\}
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  7. #7
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    Re: math league

    So do you have to count in the end?
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  8. #8
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    Re: math league

    Quote Originally Posted by victorwen28 View Post
    So do you have to count in the end?
    If you simply want the answer the please GO AWAY. You are a parasite.

    But if you want to understand, then reread the entire thread.
    If you have read questions, post them.

    But if you are simply after an answer, log off.
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  9. #9
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    Re: math league

    I want to understand how to do it, but I am not clear of your approach.
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  10. #10
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    Re: math league

    Quote Originally Posted by victorwen28 View Post
    I want to understand how to do it, but I am not clear of your approach.
    O.K.
    If I give your the set \{7,3,6,1\} how many way can you arrange those four into a strictly sorted integer?
    And what is it?
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  11. #11
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    Re: math league

    (1,3,6,7)
    only one way.
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  12. #12
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    Re: math league

    Quote Originally Posted by victorwen28 View Post
    (1,3,6,7)
    only one way.
    Correct!
    So your answer to the OP is simply
    "how many subsets of four nonzero digits are there?"
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  13. #13
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    Re: math league

    I don't quite understand how if you find the subsets of four nonzero digits, you would get them in order
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