Note: The following solution may not be the only one possible. At least one other solution has been submitted to me.

First weigh any 4 pearls against any other 4.

If one side weighs heavier than the other then:

Label the pearls on the heavy side H, the pearls on the light side L, and the 4 other pearls G. Next, weigh two H pearls and two L pearls against 2 G pearls, 1 H pearl, and 1 L pearl (HHLL vs GGHL).

If the HHLL side goes down then either one of the two H pearls on the left side from step 2 is heavy or the L pearl on the right side of step 2 is light. Finally weigh ( HL vs GG ). If the HL side goes down the H pearl is heavy, if the HL side goes up the L pearl is light, if they stay the same the other H pearl is heavy.

If the HHLL side (from step 2) goes up then either one of the two L pearls on the left side from step 2 is light or the H pearl on the right side of step 2 is heavy. Finally weigh ( HL vs GG ). If the HL side goes down the H pearl is heavy, if the HL side goes up the L pearl is light, if they stay the same the other L pearl is light.

If the two sides from step 2 stay the same you have left one H pearl and one L pearl. Weigh ( HL vs GG ). If the left side goes down the H pearl is heavy, if it goes up the L pearl is light.

If the two sides from step one stay the same then label the 8 pearls used in step 1 as G and the 4 others pearls as B. For the second weighing weigh 3 B pearls against 3 G pearls ( BBB vs GGG).

If the left side goes down one of the B pearls is heavy. Weigh them 2 of them against each other the heavy side will have the heavy pearl, if the sides stay the same the other pearl is heavy.

If the left side goes up one of the B pearls is light. Weigh them 2 of them against each other the light side will have the light pearl, if the sides stay the same the other pearl is light.

If the two sides from the second weighing stay the same then the last B pearl is heavy or light. Use the third weighing against a good pearl to determine if it is heavy or light.

Michael Shackleford, A.S.A.