Random Puzzles 

Workings

Hint
The number is less than 100.

Answer
4.

4's double is 8, and 4's quarter is 1.

Reasoning
If the missing number is N, then:

  2N = N + 7
       —
       4

Multiply throughout by 4:

  8N = N + 28

Subtract N from both sides:

  7N = 28

Divide throughout by 7:

   N = 4

Workings

Hint
You'll need to think a little laterally.

Answer
If you look very carefully, you will see that there are actually two sticks under the other seven, so you can take away eight sticks and still leave one behind.

Workings

Hint
If Alex had committed the crime, how many lies would there be?

Answer
Chris committed the crime.

Reasoning
We know that exactly 4 lies were told.

If it was Alex, then 3 lies would have been told (by those who said it wasn't Alex).

If it was Billie, then 2 lies would have been told.

If it was Chris, then 4 lies would have been told.

If it was Drew, then 3 lies would have been told.

If it was Emery, then 3 lies would have been told.

If it was Frankie, then 3 lies would have been told.

Therefore, it can only have been Chris.

Double-Checking
Since it was Chris, there were 14 truths, and 4 lies, for a total of 18 clues.

Workings

Hint
Can Q1's answer be A?

Answers
1. D
2. C
3. B
4. A

Reasoning
The easiest way to solve this puzzle is to use Q1 to check the logic.

If Q1's answer was A, this tells us that Q2's answer is B, which tells us Q3's is D, which tells us Q4's answer is B, which tells us Q1's answer is C. A contradiction.

If Q1's answer was B, this tells us that Q2's answer is A, which tells us Q3's is C, which tells us Q4's answer is C, which tells us Q1's answer is A. A contradiction.

If Q1's answer was C, this tells us that Q2's answer is D, which tells us Q3's is A, which tells us Q4's answer is D, which tells us Q1's answer is B. A contradiction.

If Q1's answer was D, this tells us that Q2's answer is C, which tells us Q3's is B, which tells us Q4's answer is A, which tells us Q1's answer is D. Which is correct, and therefore the correct answer.