# Using a balance scale exactly twice how can you weed out the fake one?

“You have nine pearls, eight are real and one is fake. All the real ones weigh the same and the fake one weighs less than the real one. Using a balance scale exactly twice how can you weed out the fake one?

Please answer ASAP. Due in Math class tomorrow. Thank you very much. You might have to “think outside the box.”

You take three and three and put them on opposite sides.

If they’re equal, then it’s in the group of three that’s not on the scales. If they’re not, then it’s the lighter group.

Take two random pearls from the group that has it. If they are equal, then the fake one is the only one in that group not on the scale. If they’re not, then it’s the lighter one.

Divide them into 3 piles of 3 pearls.

Weigh two of the piles and put one aside. If one side goes up, it has the lighter pearl. If they balance, the fake one is in the pile of 3 you put aside.

Now do the same with your pile of 3 containing the fake pearl. Weigh two of the pearls and put one aside. If one side goes up, it has the fake pearl. If they balance, it was the one pearl you put aside.

(If you follow this logic, you can figure out how to find the fake pearl among 27 pearls in 3 weighings… or 81 pearls in 4 weighings.)

Hold three in your hand. Put 3 in one pan, and 3 in the other.

If the scale is unbalanced, you will now know which side is lighter. If the scale is balanced, then you know that the lighter pearl is in the 3 pearls you are holding. Either way, you have now narrowed it down to 3 pearls.

Take all the pearls off the scale. Put the ones that you have eliminated from the possibility of having a lighter pearl aside.

Test the 3 pearls that are left in the same way that you tested the first group. Put one pearl on each side of the scale. If the scale tips, you will know which side is heavier and which is lighter. If it remains balanced, then the pearl in your hand is the one you are looking for.

Select 6 pearls and Weigh 3 on one side and 3 on the other. Select the pile that is heaviest. of they are the same weight then the Heavy pearl is in the pile you didn’t weigh.

Now you have 3 pearls one of which is the heavy pearl Select 2 pearls and compare their weight. if nether of them are the heavy ball the one not weighed was.

Step 1: Divide the pearls into groups of three.

Step 2: Weigh in two sets of three pearls (First Use)

IF the scale tips, the fake pearl is in the “higher” side of the scale, since it weighs less.

IF the scale DOESN’T tip (it stays the same – both sets of three weigh the same), the fake pearl is in the third group of pearls (the one you didn’t weigh).

Step 3: Once you have selected the group with the fake pearl, weigh in TWO of the three pearls left. (Second Use)

If the scale tips, the fake pearl is the one on the “higher” side of the scale – the one that weighs less.

IF the scale DOESN’T tip (meaning that the two pearls weighed are of equal weight), the fake pearl is the one you didn’t weigh.

Hope I helped!

1 ) You weigh 3 pearls against 3 pearls

take the lesser of the 3 pearls that did not balance and weigh 2 of them if they don’t balance the fake is the one you did not weigh

OR

If the sets of three balance the fake is of the 3 you did not weigh

and weigh 1 of each of the 3 you never weighed if they balance the fake one is the is the one you did not weigh.

this is a standard “trick” question – use linear thinking

Split into 3 groups of three

Weigh 2 of the groups – this eliminates 2 of the three groups

[since if they balance the group not weighed comtains the fake; if they don’t balance the lighter group contains the fake]

Split the remaining group of 3 into 3 groups of 1

Weigh 2 of these. If they balance then the one not weighed is the fake and if the don’t balance then the lighter is the fake