Hanoi =: 3 : 0
NB. Left argument x is the number of rings
NB. Right argument y is a pair of numbers from 0 1 2 
NB. for the start and end poles.
NB. Output is a boxed list of moves (m,n) of the top ring
NB. from pole m to pole n. 
NB. For example  
NB.               3 Hanoi 0 2  
NB. for 3 rings to go from pole 0 to pole 2.  It returns
NB. -----------------------------
NB. |0 2|0 1|2 1|0 2|1 0|1 2|0 2 |
NB. -----------------------------
:
n   =. x         NB. just a rename
n_1 =. <:x       NB. a name for n-1 
first =. {.      NB. local function for first element of a list
last  =. {:      NB. local function for last element of a list

if. n = 1
do. < y          NB. return y as a boxed pair
else. 
    v =. (-. 0 1 2 e. y) # 0 1 2   NB. locate intermediate pole

   (n_1 Hanoi (first y),v), (1 Hanoi y),  n_1 Hanoi v, last y

end.
)



NB. ====== Timing and Space ========
ts =: 6!:2 , 7!:2@]
NB.   ts '16 Hanoi 2 1'  --- boxed output
NB. 2.23474  5.77082e6
NB.   ts '16 Hanoi1 2 1' --- list output
NB. 1.4762   5.77075e6
NB.   ts '16 Hanoi2 2 1' --- stripped of comments
NB. 1.26181  2.62502e6   --- Note halved the space

NB. But the J-software supplied function H
NB. in  Studio - Labs - The Tower of Hanoi
NB.   ts '0 1 2 H 16'
NB. 0.865871  2.62483e6
NB. 
NB. The lab goes on to develop a function, H1, that has
NB. only a single, rather than a double recursion:
NB.   ts '0 1 2 H1 16'
NB. 0.00546773 3.14906e6
NB. and then develops iterative alternatives and other 
NB. ways of shortening the execution time to get
NB.   ts 'H5 16'
NB. 0.00490621  1.57382e6
NB. =================================