Random Puzzles 

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
The first letter can only be B.

Answer
A badger.

Reasoning
My first is in bridge, but not in ridge = B

My second is in awake, and in mistake = A K E

My third is in danger, but not in ranger = D

My fourth is in strange, and in orange = R A N G E

My fifth is in spline, and in nine = I N E

My last is in river, and in diver = R I V E

Workings

Hint
How many sweets in total are there?

Answer
1 in 15.

Reasoning
In total, there are 390 sweets in the jar, and 26 of them are blue.

So the chance of picking blue is 26 in 390 = 1 in 15 = 6.66%.

Workings

Hint
Oval becomes Opal.

Answers
Paperweight.
opal past spin melt wren swab mess find aged shed stay