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Thread: Number Problem

  1. #1
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    Number Problem

    Find a number such that if we replace the first digit of the number with the last digit...the number doubles itself.

    Last edited by smart_coder; 03-12-2007 at 05:36 AM.

  2. #2
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    Re: Number Problem

    i think the answer is 00. I can't able to find the other answer..smartcoder give some clue... tell me howmany digit number that was..

    ---------------
    suresh


  3. #3
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    Re: Number Problem

    Its not 0. I cnt tell u the number of digits!!


  4. #4
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    Re: Number Problem

    Correction in my problem :

    Find a number such that if we shiftthe first digit of the number with the last digit...the number doubles itself.

    like if the number is abcdef
    the doubled number should be fabcde


  5. #5
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    Re: Number Problem

    hi smart coder,

    It is a time for giving your solution here....Otherwise give some other clue to solve this puzzle...

    -------------------
    suresh


  6. #6
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    Re: Number Problem

    there are 9 solutions each of 18 digits


  7. #7
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    Re: Number Problem

    Here is the answer for your question.....

    Number : 052631578947368421

    But this very difficult to find the answer....Here is some of the numbers i am work it out....

    First of all i found the first digit should not greater than 4. Because if we use 5, after adding the number it is going to be extra one digit.

    First i am trying the following numbers....

    47389
    double: 94778
    one shift: 94738
    difference: 40


    42068
    double: 84136
    one shift: 84206
    difference: 80

    36747
    double: 73494
    one shift: 73674
    difference: 180

    31526
    double: 63052
    one shift: 63152
    difference: 100

    26345
    double: 52690
    one shift: 52734
    difference: 44

    21044
    double: 42088
    one shift: 42104
    difference: 16

    15763
    double: 31526
    one shift: 31576
    difference: 50

    10542
    double: 21084
    one shift: 21054
    difference: 30

    051
    double: 102
    one shift: 105
    difference: 3
    Here i found i am going to the right way. In that time smart coder give the clue that is 18 digit number.

    0521
    double: 1042
    one shift: 1052
    difference: 10

    052621
    double: 105242
    one shift: 105262
    difference: 20

    0526321
    double: 1052642
    one shift: 1052632
    difference: 10

    ...
    ..

    Using the same way finally i got the answer...But i don't know, is there any way to find the solution easily ?

    --------------------
    suresh


  8. #8
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    Re: Number Problem

    yes there is an easy way out, so i am putting up the solution

    select any digit from 1 to 9. Suppose u selected 1.

    Now I will double it. I get 2.
    So my unit's digit is 2. again double it, I get 4
    Now my number becomes 42.
    Again I double 4.I get 8.
    Now my number becomes 842.
    So the logic is pick the leftmost digit ...double it and make it as the new leftmost digit(keep the carries aside)

    now i take 8. Double it. I get 16. Now my number is
    6842. carry = 1.
    I take 6. double it. I get 12. Adding carry ( + 1) . I get 13. Now my number is
    36842. carry = 1.

    If we go on like dis we will reach at a stage like dis

    5263157894736842 (carry = 0 )
    take 5. double it. we get 10. Now my number is

    105263157894736842 (carry = 0)
    We end up wen we get the leftmost digit as the starting digit which we selected ( in this case it was 1) and carry = 0.

    So here we get our number. U can check the condition over dis number.
    Similarly select another digit initially and do the whole procedure with that digit. So there are 9 different answers.
    Hope it was intresting!!


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