Numerical puzzle

  • Thread starter furnis1
  • Start date
  • #1
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Homework Statement


Im having problem of even starting this question:

"Determine the positive integer N = abcdef such that 6N = defabc"

any ideas?

Homework Equations





The Attempt at a Solution

 

Answers and Replies

  • #2
1,341
3
[tex]6N = defabc = abcdef = N[/tex]

6N doesn't equal N unless it's 0. The only solution is 0 which is not a positive integer.

Or am I missing something really stupid?
 
  • #3
5
0
actually i ended up solving it
abc = 142 and def = 857

....abc and def are just the digits in the question. but thanks!
 
  • #4
dynamicsolo
Homework Helper
1,648
4
Actually, anyone who recognizes the decimal expansions of 1/7 and 6/7 might suspect immediately that this is an answer... (Ah, but is it unique?)

Feldoh, this type of puzzle is what is referred to as a cryptarithm. Letters stand in for digits and the prospective solver is supposed to "decode" the arithmetic problem. In classical form, this problem would be posed as

ABCDEF
x 6
______
DEFABC

The question does not say that 6N = N , but that 6N is a digital rearrangment of N.
 
  • #5
1,341
3
Regardless I think the question could be worded better...
 
  • #6
dynamicsolo
Homework Helper
1,648
4
It did strike me that the intent of the problem might be obscure to anyone not familiar with this kind of puzzle.
 

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