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 working backwards.

Answer
7,340 metres.

Reasoning
Stage 5's clue tells us that 150m was left. So the distance left at the start of Stage 4 must have been:
Dist4 = Dist4 + 75 + 150
        —————
          2

Which simplifies to give Dist4 = 450m.

Stage 3's clue tells us that 450m was one quarter of the remaining distance, so Dist3 = 1,800m.

Stage 2's clue tells us that the distance at the start of Stage 2 was:
Dist2 = Dist2 + 35 + 1800
        —————
          2

Which simplifies to give Dist2 = 3,670m.

Stage 1's clue tells us that 3,670m was half the overall distance, which means the entire ride was 7,340m.

Double-Checking
Starting with 7,340m:
Stage 1: cycled 3,670m, leaving 3,670m

Stage 2: cycled 1,870m, leaving 1,800m

Stage 3: cycled 1,350m, leaving   450m

Stage 4: cycled   300m, leaving   150m

Stage 5: cycled   150m, leaving     0m

Workings

Hint
Light travels over 186,000 miles each second.

Answer
Miles travelled by light in a second.

Reasoning
Light travels over 186,000 miles per second.

There are 2.54 cm in an inch, 12 inches in a foot, 3 feet in a yard, and 1760 yards in a mile. So there are 2.54 x 12 x 3 x 1760 = 160,934.4 cm in a mile.

Workings

Hint
How many letters does each name have?

Answer
Simon married Teresa: their names have 11 letters when combined.