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Some Summed Digits In A 9-Digit Positive Integer

  1. Nov 19, 2008 #1
    Determine a 9-digit positive integer that uses each of the decimal digits from 1 to 9 exactly once, such that:

    (i) The sum of the digits 1 and 2 and all the digits between them is 9.

    (ii) The sum of the digits 2 and 3 and all the digits between them is 20.

    (iii) The sum of the digits 3 and 4 and all the digits between them is 45.

    (iv) The sum of the digits 4 and 5 and all the digits between them is 18.

    (v) The sum of the digits 8 and 9 and all the digits between them is more than 32.

    (vi) The 8th digit is less than the 2nd digit.
     
  2. jcsd
  3. Nov 19, 2008 #2
    495162783
     
  4. Nov 20, 2008 #3
    Well done JS !!!

    I came across this problem in a puzzle periodical. However, the original version only provided clues (i) to (iv). I added clues (v) and (vi) on my own with a view to eliciting an unique solution.

    I am just thinking aloud, but keeping all the other conditions unaltered, that is, 9-digit positive integer, using all the digits 1 to 9 exactly once, and so on ……, are there positive nondecimal integer base(s) A, with 11<= A <= 16, such that A gives at least one valid solution to the given problem !!!
     
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