>>There are 6 balls: 2 red, 2 blue and 2 white. One of the balls of each color is slightly lighter than the second ball of the same color (you can name these two weighs as A & B). You need to sort out all the balls. You can weigh them only 2 times on a balance scale.
>
>Sorry I didn't respond to this earlier.
>I've never had a good chance to work on it.
>I'm going to name each ball by their column and a number.
>R1, R2
>B1, B2
>W1, W2
>
>
>In weighing A:
>I will weigh the following:
>R1,B1 --- W1,B2
>
>Case 1 - A EQUAL
>We will take the easiest possibility first.
>If weighing A is equal
>
>I will then weigh B:
>R2 --- W2
>
>They cannot be equal because we know
>1. Either B1 is lighter or B2 is lighter.
>2. Since weighing A is equal:
> a. Either R1 is lighter and off setting the lighter ball B2
> b. Or W1 is lighter and off setting the lighter ball B1.
> c. If both R1 and W1 were lighter the scale would have to tip either up
> the 2 combined light balls R1 AND B1 or W1 AND B2 would be lighter than
> the combination on the other side.
>
>This leaves only 2 possibilities from weighing B:
>The left side (R2) is lighter.
>
>This means, since R2 is obviously the lighter ball that R1 is normal.
>That means as described above. That W1 must be lighter and be offsetting ball B1.
>
>This leaves us with R2, W1, and B1 being the lighter balls.
>
>
>The other possibility is that the right side is lighter in Weighing B:
>The right side (W2) is lighter.
>
>This means, since R1 is obviously the lighter ball that R2 is normal.
>That means as described above, that R1 must be lighter and be offsetting ball B2.
>
>This leaves us with R1, W2, B2 being the lighter balls.
>
>
>
>
>CASE 2 - A - RIGHT SIDE LIGHTER
>Now we will tackle the harder cases.
>In weighing A ( R1,B1 --- W1,B2 )
>The Right side is lighter ( W1, B2 ).
>
>We know the following:
>1. B1 is normal.
>2. B2 is lighter.
>If B1 was lighter, the only way for the right side to be lighter is for both W1 and
>B2 to both be lighter. This is not possible, because both B1 and B2 cannot be lighter.
>
>In weighing B we will:
>W1,B1 --- W2,R1
>
>If B is equal:
>1. W2 can't be lighter because W2 can't be offset by W1 or B1 which is normal.
>2. This means that W1 is lighter and is being offset by the R1.
>
>This leaves us with R1, W1, B2 as the lighter balls.
>
>
>If in B the left side is lighter ( W1, B1 )
>1. W1 must be lighter, since B1 is normal.
>2. Both W2 and R1 are normal, because neither offset W1.
>
>This leaves us with R2, W1, B2 as the lighter balls.
>
>If in B the right side is lighter ( W2, R1 )
>1. W2 must be lighter and R1 must be normal.
> a. If both W2 and R1 was lighter then that would make W1 normal
> and in weighing A B2 would have been offset by R1 making both
> sides equal.
> b. If R1 was lighter and W2 was normal then in weighing B R1 would
> have been offset by W1 and both sides would be equal.
>
>This leaves us with R2, W2, B2 as the lighter balls.
>
>
>
>
>CASE 3 - A - LEFT SIDE LIGHTER
>This is the same as in case 2 but in reverse
>and will only be included for completeness.
>In weighing A ( R1,B1 --- W1,B2 )
>The Left side is lighter ( R1, B1 ).
>
>We know the following:
>1. B1 is lighter.
>2. B2 is normal.
>If B2 was lighter, the only way for the left side to be lighter is for both R1 and
>B1 to be lighter. This is not possible, because both B1 and B2 cannot be lighter.
>
>In weighing B we will:
>W1,R2 --- R1,B2
>
>If B is equal:
>1. R2 can't be lighter because R2 can't be offset by R1 or B2 which is normal.
>2. This means that R1 is lighter and is being offset by the W1.
>
>This leaves us with R1, W1, B1 as the lighter balls.
>
>
>
>If in B the right side is lighter ( R1, B2 )
>1. R1 must be lighter since B2 is normal.
>2. Both W1 and R2 are normal, because neither offset R1.
>
>This leaves us with R1, W2, B1 as the lighter balls.
>
>
>If in B the left side is lighter ( W1, R2 )
>1. R2 must be lighter and W1 must be normal.
> a. If both W1 and R2 was lighter then that would make R1 normal.
> and in weighing A B1 would have been offset by W1 making both
> sides equal.
> b. If W1 was lighter and R2 was normal then in weighing B W1 would
> have been offset by R1 and both sides would be equal.
>
>This leaves us with R2, W2, B1 as the lighter balls.

The explanation is a little bit complicated and since it was long time ago I already forgot the solution, so I would have to solve it myself