January 25th, 2012, 12:08 PM

Shift Cipher No. of nonFixed Mapping substitution tables possible.
A substitution table is said to be a fixed mapping if at least one of the characters maps to itself, i.e. A>A.
How many substitution tables will be there where not even a single alphabet maps to itself.
My solution:
I first tried to find out number of substitution tables with fixed matching.
If only 26 alphabet maps to itself No. of substitution tables with fixed mapping will be 1
If only 25 alphabets maps to itself No. of substitution tables with fixed mapping will be 0
If only 24 alphabets maps to itself No. of substitution tables with fixed mapping will be (26C2)
If only 23 alphabets maps to itself No. of substitution tables with fixed mapping will be (26C3)*2
If only 22 alphabets maps to itself No. of substitution tables with fixed mapping will be (26C4)*9
If only 22 alphabets maps to itself No. of substitution tables with fixed mapping will be (26C5)*44
The main problem is that there is not a general formula for calculating no of fixed mapping if we know that a particular no. of alphabets map to themselves.
If you have any other solution/approach to this problem, please share it.
January 27th, 2012, 01:04 AM

Rewrite your post using more precise definitions.