Math/logic question: Ten pearls?

divide the pearls into 3(a)-3(b)-3(c)-1.

weigh a against b and b against c.

If everything balances, the tenth pearl is fake.

a and b balance but b and c don't, c must contain the fake and you'll know if it's lighter or heavier from the way the scale tips.

If a and b don't balance but b and c do then a must contain the fake pearl and again you'll know whether or not it was heavier or lighter.

If they both don't balance, then b contains the fake and once again you'll know if it's heavier or lighter.

Take the group of three containing the fake and balance any two of them. If they don't balance, use your knowledge of whether the fake is heavier or lighter to identify the fake. If they do balance, the one you didn't weigh is the fake.

Put 3 on each side and leave 4 aside.

If the scale levels, then the fake is in the group of 4 on the side, and the 6 you measured are all real. Put 3 out of the 4 from the side on the right side of the scale(leaving one alone) against three of the real ones from the first measurement on the left. If the scale is level, the fake one is sitting by itself and you're done. If the scale is not level but the right is heavy, then the fake is heavier. If the right side is lighter, then the fake is lighter. If the scale is not level, we know that the fake is contained in the 3 on the right side. Pick any two weigh them. If they are level, then the 3rd pearl is fake. If they aren't level, then either the lighter or heavier is the fake based on what you learned from earlier.

If the scale is not level, then the 4 you put aside are good and the fake is in the left 3 or right 3. Leave one group of 3 on the scale, and put 3 of the good ones on the other side. If the scale is level, then the fake is in the other 3 you put aside. If the scale is off level, then you know the fake is in the group still sitting on the scale from before, and you also know if it's light or heavy. Follow the plan for picking the fake out of 3 from above.

place one pearl on one side, and one on the other. If they are equal, place one in the equal pile. Continue until you find a pearl that doesnt balance to any in the equal pile, say #8. Weigh it against the other 9 and if none of them balance, #8 is the counterfeit, that is the counterfeit. However, you may possibly pick the counterfeit first. So weigh all the other 9 pearls against the 1st pearl. If none of them balance, the 1st pearl is the counterfeit.

I'm not much of a Pearl Jam fan. Eddie's voice is a bit crap. I like Black, though. Try Smashing Pumpkins, Alice in Chains and Soundgarden if you like Pearl jam. =D

Here's the answer to the same problem, but using 12 instead of 10. http://mathproblems.info/prob84a.htm

I'm sure a similar technique could be used.

clarification - you can only weigh three at a time

or three on a side - 6 at a time?

or only weigh three totally

here this works for 12 ten should be easier.

haha...take the scale and smash 'em...which ever one breaks the easiest is the fake :D

bobcat's explanation was excellent