Here is a BASIC version for the HP-71b, one of my favorite calculators. It is much faster than the 32sii version, probably because it doesn't have to decode multiple numbers stored in a register.

HP 71b program to determine 15 puzzle solvability

10 destroy all

20 integer a(16)

30 data 11,5,14,7,15,2,9,4,6,0,1,13,10,3,12,8

40 for i=1 to 16

50 read a(i)

60 if a(i)=0 then let b=ip((i+3)/4)

70 next i

80 for i=1 to 15

90 for j=i+1 to 16

100 if a(j)<>0 and a(j)<a(i) then let b=b+1

110 next j

120 next i

130 if mod(b,2)=0 then disp "solvable" else disp "unsolvable"

140 disp "inversions = ";b

Nice-- and easy on the eyes.. I started a 50g program that uses PUT,PUTI,GET, LOC and REPL. It's compact, but incomplete as yet.