http://www.spoj.com/problems/CARD/

gistfile1.txt

i) Each shuffle is described by n numbers t1,t2,...,tn

A shuffle defines a reindexing of the cards

```
given cards C = [ a b c d e]
and shuffle S = [ 2 3 4 5 1]

S(C) = [b c d e a]

given shuffle S2 = [5 4 3 2 1] 

S2(C) = [e d c b a]

```

Note that these shuffles can be composed:

```
S2(S(C)) = S2( [b c d e a] )
	= [ a e d c b ]

S(S2(C)) = S( [e d c b a] )
	= [d c b a e]

S(S(S2(C))) = S([d c b a e])
	 = [c b a e d]

```

Thus by composing the two shuffles S and S2,  we can perform new shuffles (without learning them)

```
S3(C) = [ 1 5 4 3 2 ] = S2(S(C))
S4(C) = [ 4 3 2 1 5 ] = S(S2(C))
S5(C) = [ 3 2 1 5 4 ] = S(S(S2(C)))
```

the shuffler know shuffle S, and is trying to learn a second shuffle ci such that the various compositions of these shuffles maximizes the number of knows shuffles from a given list (c1,c2,...ck)