Random Puzzles 

Workings

Hint
The answer isn't 9!

Answer
One big one!

Workings

Hint
What's a mathematical way to describe placing a 9 at the beginning?

Answer
23,076.

Reasoning
Placing the 9 at the beginning is equivalent to adding 900,000 (for example, 12,345 + 900,000 becomes 912,345).

Placing the 9 at the end is equivalent to multiplying by 10 and adding 9 (for example, 12,345 x 10 + 9 becomes 123,459).

Let's call the unknown number k, and we know that one of these numbers is 4 times the other, so:

 k + 900,000 = 4 x (10k + 9)

 k + 900,000 = 40k + 36

900,000 – 36 = 40k – k

     899,964 = 39k

899,964 ÷ 39 = k

Therefore, k = 23,076.

Double-Checking
923,076 = 4 x 230,769.

Workings

Hint
A very common sequence.

Answer
Violet.

From the colours of the rainbow.

Workings

Hint
Can Q1 be A?

Answers
Q1. B
Q2. B
Q3. A
Q4. B

Reasoning
Q1 can't have A as its answer (otherwise it would contradict itself).

If Q1's answer was C (meaning Q4's answer was A), then Q3's answer would be C. However, Q2's answer should now be A, but this isn't allowed by Q1 (as Q4 is the first answer with A). This is a contradiction.

Therefore, Q1's answer is B (meaning Q3's answer is A).

For Q2's answer to be C, Q4's answer would have to be A, which would contradict Q4. Therefore, Q2's answer is B making Q4's answer B.