[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.

[Guest]

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.

[Guest]

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.

[Guest]

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.

[Guest]

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.