Brain Teasers and Puzzles 

Workings

Hint
One of answers involves royalty.

Answer
Prince, princes, princess.

Bra, bras, brass.

A similar change is care, cares, caress, but these are not nouns.

Workings

Hint
Try working backwards.

Answer
148.

Reasoning
A number that is divisible by 3 has digits that add up to a number that is also divisible by 3 (for example, 123 is divisible by 3).

So we can look for the first number where 4 + 4 + 4 + 4 + 4 + … is divisible by 3, which is 4 + 4 + 4, and 444 ÷ 3 = 148.

Alternative Reasoning
Let's try the possible answers in order:

  4 ÷ 3 = 1.3333
 44 ÷ 3 = 14.6666
444 ÷ 3 = 148

Double-Checking
148 x 3 = 444.

Workings

Hint
This is quite a common alphabet.

Answer
Z.

From Zeta, first letters of the Greek alphabet, alpha, beta, gamma, delta, epsilon, zeta, eta.

Workings

Hint
Water turns to?

Answer
Water.

The next coldest state of each.