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Digits 1-9 (Posted on 2002-06-05) Difficulty: 3 of 5
Can you arrange the digits 1-9 in any order so that:
  • The number formed by the first two digits is divisible by 2.
  • The number formed by the first three digits is divisible by 3.
  • The number formed by the first four digits is divisible by 4
  • and so on up to nine digits...
  • See The Solution Submitted by Rhonda Wendel    
    Rating: 3.1429 (7 votes)

    Comments: ( Back to comment list | You must be logged in to post comments.)
    Hints/Tips Eliminate more; Test less(Part 2) | Comment 6 of 13 |
    (In reply to Eliminate more; Test less(Part 1) by TomM)

    Returning to Constraint 3, in the first case, digits 1 and 3 must be 1 and 7 in some order, and digits 7 and 9 must be 3 and 9 in some order (four possibilities: 147258369, 741258369, 147258963, 741258963)

    In the second case, if 1 is in position 1 or 3, then 7 must be in position 7 or 9, and vice versa. Similarly with 3 and 9. We end up with 16 possibilities.

    These constraints guarantee the number meeting all of the initial conditions except two. The first eight digits are only guaranteed to be divisible by 4, not by eight, and nothing is guaranteed concerning the first seven digits.

    For the first eight digits to be divisble by 8, digits 7 and 8 must be 16, 32, 72, or 96.

    This reduces the possibilities in the first case from four to two: (147258963 and 741258963), and in the second case, from sixteen to eight.
      Posted by TomM on 2002-06-07 14:54:18

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