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Posers and Puzzles

Posers and Puzzles

  1. 04 Aug '05 14:26
    When a positive integer N is written in base 9, it is a two-digit number. Wnen 6N is written in base 7, it is a three-digit number obtained from the two-digit number by writing 4 to its right. Find the decimal representations of all such numbers N.

    Does that mean the two-digit number of base 9 and the three-digit number of base 7 both contain one "4"?
    Please explain.
  2. 04 Aug '05 15:02
    Originally posted by ardnas
    When a positive integer N is written in base 9, it is a two-digit number. Wnen 6N is written in base 7, it is a three-digit number obtained from the two-digit number by writing 4 to its right. Find the decimal representations of all such numbers N.

    Does that mean the two-digit number of base 9 and the three-digit number of base 7 both contain one "4"?
    Please explain.
    By 6N do you mean 6xN or the 6N (as in concatenation of N after 6)?
  3. Standard member PBE6
    Bananarama
    04 Aug '05 17:02
    Originally posted by ardnas
    When a positive integer N is written in base 9, it is a two-digit number. Wnen 6N is written in base 7, it is a three-digit number obtained from the two-digit number by writing 4 to its right. Find the decimal representations of all such numbers N.

    Does that mean the two-digit number of base 9 and the three-digit number of base 7 both contain one "4"?
    Please explain.
    OK, here's my list of numbers (decimal - Nbase9/6*Nbase7):

    10 - 11/114
    24 - 26/264

    So it's not necessary to have a 4 in both numbers. Explaination to follow when I figure it out.


  4. 04 Aug '05 17:10
    There is only one decimal number that fits this construct. The two digit number does not contain a 4. Should I PM you with the number or just post it?
  5. 06 Aug '05 07:31
    Originally posted by jebry
    There is only one decimal number that fits this construct. The two digit number does not contain a 4. Should I PM you with the number or just post it?
    Please email me with it, thanks!