Another way of solution:

Cut a quarter of each ball, giving us 12 pieces i.e 3 balls. Each piece of quarter should weigh 2.5 grams.

-Weigh any two balls(Attempt one).

• If two balls (8 pieces) left in doubt. So we weigh any one ball (Attempt two)

• If one ball left faulty(4 pieces), Cut each of the piece and take 1/2 of the 1st piece 1/4th of second, 1/8th of 3rd and 1/16th of 4th piece. which should give: 1.25, 0.625, 0.3125 and 0.15625. And a faulty one quarter piece(9/4 = 2.24 grams): 1.125, 0.5625, 0.28125 and 0.140625. So by adding the combination we get unique weight and can determine which piece is faulty. (Attempt three)

(Cutting the pieces in half is considerably easy(in absence of any accurate tools), which is why it would be easier to get 1/4th and 1/8th of a piece. And even simplifies the calculations to some extent.)

These paradoxical statements are too twisted to bite.

for eg: "I am always lying" is this person speaking truth or lie?

The general tendency of people using the paste is the amount poured accordance to the length of the bristle of the toothbrush. If we consider that factor here that length of the paste poured remains constant, then we can say the diameter of the tube is in taken in consideration, as we can determine the volume of paste used on one squeeze. This will provide a rough calculations giving you using lesser amount used as compared with tube with larger tube.