I know that the N queens algorithm can be long. Using code I found on the HP museum website by T. Klemm for another calculator, the HP 17BII for 4 queens, I made modifications for 8 queens. My code is a total of 149 lines and runs in about 6.5 seconds (faster than the 7+ time I saw in another post).
First, do XEQ nq8. nq8 will call the nz subroutine. To see the values, recall registers 01 to 08. The integer part holds the row number for each queen.
You should get 1, 5, 8, 6, 3, 7, 2, 4.