MathDB

We have four registers,

R_1,R_2,R_3,R_4

, such that

R_i

initially contains the number

i

for

1\le i\le4

. We are allowed two operations:
[*] Simultaneously swap the contents of

R_1

and

R_3

as well as

R_2

and

R_4

.
[*] Simultaneously transfer the contents of

R_2

R_3

, the contents of

R_3

R_4

, and the contents of

R_4

R_2

. (For example if we do this once then

(R_1,R_2,R_3,R_4)=(1,4,2,3)

.)
Using these two operations as many times as desired and in whatever order, what is the total number of possible outcomes?

Problem Statement