Random Puzzles 

Workings

Hint
One of the words starts and ends with T.

Answers
eve    = level able   = tablet carve  = scarves as     = ease, hash, sass on     = gong, sons ode    = codec, modem elude  = deluded ape    = lapel ate    = dated, rater rod    = erode

Workings

Hint
Think of Roman numerals.

Answer
Delta.

Take the Roman numerals in sequence, and convert to the phonetic alphabet.
  1 = I = India
  5 = V = Victor
 10 = X = X-Ray
 50 = L = Lima
100 = C = Charlie
500 = D = Delta

Workings

Hint
What do the 3 numbers add to, and multiply to, so far?

Answer
$0.50.

Reasoning
The three prices add to 1.50 + 3.00 + 4.00 = 8.50.

The three prices multiply to 1.50 x 3.00 x 4.00 = 18.00.

You might be able to see that adding another 0.50 will take the total to 9.00, and multiplying by another 0.50 will take the product to 9.00.

The answer can also be found using algebra. If we call the missing price P, we have:
1.50 + 3.00 + 4.00 + P = 1.50 x 3.00 x 4.00 x P

    8.50 + P = 18.00 x P

        8.50 = 18.00 x P − P

        8.50 = 17.00 x P

8.50 ÷ 17.00 = P

           P = 0.50.

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.