Question

Let it be a sequence of N elements that can be ordered. At each draw, all elements from the sequence are shuffled. Example with N=8:

draw1=(e4,e3,e0,e6,e1,e7,e2,e5)draw2=(e7,e2,e0,e1,e8,e3,e6,e4)draw3=(e4,e0,e3,e2,e6,e5,e7,e1)...

Within a sequence, elements can be pairwise compared. Since there are N! different orderings, each draw has an entropy of log2(N!) bits.

Now, let's modify the system such that there is two sequences of N/2 elements. At each draw, elements are shuffled and half of them goes to the first sequence and the other half to the second sequence. Example with N=8:

draw1={(e4,e3,e7,e0),(e2,e1,e5,e6)}draw2={(e6,e3,e1,e7),(e5,e0,e2,e4)}draw3={(e7,e1,e5,e4),(e0,e6,e2,e3)}...

What is the entropy of such system if the elements can only be compared between the two sequence and not within the same sequence? For example, in draw1, e4 can only be compared to e2, e1, e5 or e6.​

Answer 1

Answer:

Step-by-step explanation:

WOW THIS IS HARD!

NO IDEA SORRYY