Random Puzzles 

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
Try removing the spaces between the numbers.

Answer
48 and 11.

Reasoning
These are the squares of numbers without the correct spacing.

   1 4 9 16 25 36 49 64 81 100

with no spaces becomes:

   149162536496481100

broken into blocks of two:

   14 91 62 53 64 96 48 11 00

So the next two in the sequence are 48 and 11.

Workings

Hint
How many reservoirs can each drain in 36 hours?

Answer
7 hours and 12 minutes.

Reasoning
We can use a time that 12 hours and 18 hours both fit in to, in 36 hours:

   6 large pipes can drain 3 reservoirs.
   6 small pipes can drain 2 reservoirs.

Therefore, together, 6 large and 6 small pipes can drain 5 reservoirs.

36 hours ÷ 5 = 7.2 hours for one reservoir.

7.2 hours = 7 hours and 12 minutes for one reservoir.

Workings

Hint
There are 12 inches in a foot, and 1,760 yards in a mile.

Answer
Feet in a 20-mile walk.

Reasoning
There are 12 inches in a foot, 3 feet in a yard, and 1,760 yards in a mile:

   square inches in a piece of carpet 15 yards by 5 yards
      (15 x 3 x 12) x (5 x 3 x 12) = 97,200 square inches.

   feet in a 20-mile walk
      20 x 1760 x 3 = 105,600 feet.