Random Puzzles 

Workings

Hint
There are two sequences.

Answer
26.

There are two alternate series, starting with the first two numbers, and each formed by doubling the preceding number in its own series and subtracting 2.

Workings

Hint
There is only one way to make the middle 25.

Answer
 

Workings

Hint
The number is less than 20.

Answer
8.

Reasoning
We need a number (N) such that:

2 x N = 14 +  N
             ———
              4

Multiply throughout by 4 to give:

8 x N = 56 + N

So:

7 x N = 56

So N = 8.

Double-Checking
Its double is 16.

Its quarter is 2.

So its double is fourteen more than its quarter.

Workings

Hint
How can we write this time and date?

Answer
The time and day became:

12:34 5/6/78 (in UK format)

In US format, this happened on the 6^th of May.