superprismatic Posted September 21, 2009 Report Share Posted September 21, 2009 The fraction 1/N (for a positive integer N) is found to have a decimal representation which is cyclic with period 26. The digits proceeding left to right from the decimal point, are assigned in order to the letters from A to Z. Note that by this scheme a digit may stand for more than one letter. The message: "A cab is a taxi" enciphered by means of these equivalents becomes: 0 100 54 0 3075. Find N. Quote Link to comment Share on other sites More sharing options...
0 Guest Posted September 21, 2009 Report Share Posted September 21, 2009 583. Basically, the number is: 1/N = .001xxxxx5xxxxxxxxx43xxx7xx... = 1xxxxx5xxxxxxxxx43xxx7xx/(1026 - 1) By looking at factors of 1026 - 1 (I just checked those under 1000, as it is clear that N must be not more than 1000 since it has only two leading zeros), we can get to N. Quote Link to comment Share on other sites More sharing options...
0 Guest Posted September 21, 2009 Report Share Posted September 21, 2009 N = 0. All credit to methinks though just didn't want to do all the math my self. Thought it is very true it had to be between 500 and 1000. I bet there is a way to do this not just through brute force. Lemme think on it. Quote Link to comment Share on other sites More sharing options...
0 Guest Posted September 21, 2009 Report Share Posted September 21, 2009 583. .00171526586620926243567753 repeated. Has to be beween 501 and 1000. You can get it down to about 50 numbers where i=5. Then slightly brute force from there. Quote Link to comment Share on other sites More sharing options...
0 Guest Posted September 21, 2009 Report Share Posted September 21, 2009 Yeah I just ended up using brute force to find the factors of 10^26-1 between 500 and 100. 583 711 859 869 I still say N is 0 though. Quote Link to comment Share on other sites More sharing options...
Question
superprismatic
The fraction 1/N (for a positive
integer N) is found to have a decimal
representation which is cyclic with
period 26. The digits proceeding
left to right from the decimal point,
are assigned in order to the letters
from A to Z. Note that by this
scheme a digit may stand for more
than one letter. The message:
"A cab is a taxi" enciphered by
means of these equivalents becomes:
0 100 54 0 3075. Find N.
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