# Any Math Studs Out There?

will someone please explain how to solve this problem

there are 8 silver coins and one counterfeit coin that looks like a silver coin but actually weighs slightly less than the others.

by using a balance scale to compare coins (or groups of coins), how can you determine the counterfeit coin with just 2 weighings???

i shall give the first person to solve and explain the answer, best answer!

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Divide the coins into 3 groups, 3 coins in each group.

Take two of the three groups and put one on either side of the scale (ignore the last three coins for now).

If the scales balance, then obviously the counterfeit coin is in the last group of three, in which case you disregard the rest and just concentrate on the last group of three. Pick two of the three coins and put them on the scale. If they balance, then the last coin is the counterfeit. If one scale is lighter, obviously it’s the counterfeit. There we go, problem solved in 2 steps.

If the scales don’t balance when you place your groups of 3 coins upon them, the solution is still easy. The lighter of the two groups contains the counterfeit, and now you have three coins to choose from again, so use the method explained in the previous paragraph. There, all done!!

Divide the 9 coins into 3 groups of 3

Using a balance scale, put 3 of the coins on one side, and 3 coins on the other. If the scale balances you know that all the coins are the same. If one side is heavier, you know that the heavier coin is one of those 3. Select a coin for each side of the balance scale. Again if the

scale balances, the coin you did not select is the heavier otherwise the balance scale will tip to the heavier coin.

Then remove those 6 and select 2 coins. Put 1 coin on either side of the balance scale, If the scales balance, you know the one coin not selected is the heavier coin, but if the scales don’t balance, you know the heavier coin.

Why does this work?? Because 3 balances and 2 weighs = 0 or

3^2 = 9

ok so, there are many possibilities so let me try to break it down for each scenario. lets color the coins to make it easier to understand. 3 GREEN, 3 RED and 2 GOLD

1st weigh:

Put the 3 RED coins on the left of the scale and the 3 GREEN coins on the right of the scale.

Now here come the different possibilities.

a) Lets say that the scale was balenced. so the counterfeit coin can’t be one of those. So it’s one of the 2 GOLD coins.

2nd weigh:

Put one GOLD coin on each side and which ever side is lighter is the counterfeit coin.

b) but what if the scale wasn’t balanced on the first weigh? Ok so what you want to do then is take whichever side weighed less and keep them because the counterfeit coin must be among them. Let’s say the RED coins weighed less.

2nd weigh:

Put 2 of the 3 RED coins on the scale. If it is balanced then the counterfeit coin is the coin you left out. If they are not balanced then the lighter side is the counterfeit coin.