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find the total number of subtraction remaining 1111?

  1. Jul 1, 2017 #1
    1. The problem statement, all variables and given/known data
    15_Mat_B_1.5.png

    2. Relevant equations


    3. The attempt at a solution
    5 digits minus 4 digit remaining 11111?
    if the 5 digit = 20000
    and the 4 digit = 8889
    so remaining 11111

    digits 1 to 9 have been used?
    what am I supposed to do?
     
  2. jcsd
  3. Jul 1, 2017 #2

    SammyS

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    Wow. The wording of this problem had me stumped. I had to read it many times before maybe figuring out what it's asking.

    I think it must mean:

    Suppose A and B have 5 and 4 digits respectively, and that A − B = 11111 . Furthermore, all digits 1 - 9 are used in writing the combination of A and B.
    What are all of the possible sets of numbers A and B for which this is true?​
    .
     
  4. Jul 2, 2017 #3
    I get 19753 - 8642 = 11111. But i dont know, total number of substractions? 8+6+4+2 = 20... the key answer different
     
  5. Jul 2, 2017 #4

    SammyS

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    As long as each pair, {9, 8}, {7, 6}, {5, 4}, {3, 2} is lined up together, you will have the correct result.

    Can you show that the leading digit in the 5 digit number can't be a 2 ?
     
  6. Jul 2, 2017 #5
    The leading number cant be 2, because that leading number wont be substracted , thus is 1. ?
     
  7. Jul 2, 2017 #6

    mfb

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    How do we get a "number of subtractions" that way?

    The way I interpreted it, we start with a 5-digit number, let's say 35791, and then subtract a 4-digit number, let's say 2468, repeatedly until the result is 11111:
    35791-n*2468= 11111
    This has n=10 as solution.

    With that interpretation we don't get a unique solution, on the other hand, as we have n=10 and n=1 as examples already.
    It is a bit more complicated as the 4-digit number could start with 9.

    Do you know the intended answer?
     
  8. Jul 16, 2017 #7
    Poorly worded questions honestly but I think that mfb's interpretation is probably correct
     
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