Random Puzzles 

Workings

Hint
Look at the start of each word.

Answer
augment.

The first three letters are the same as the first three letters of the months in order.

Workings

Hint
The answer is something to do with time.

Answer
The order is based on the length of day of the planet in Earth hours and days.

Jupiter has the shortest day (≈ 9 Earth hours), and Venus has the longest day (≈ 243 Earth days).

Workings

Hint
Is a million grains of sand a heap?

Answer
We can probably agree on two things:

A million grains of sand is a heap.
If we remove one grain of sand from this heap, we will still have a heap.
We can now keep repeating (2) until we only have a single grain of sand remaining.

Is this a heap? Clearly not. But what went wrong with our thinking?

This is called the Sorites paradox (soros being Greek for "heap") and is a classic paradox that has no real answer.

Both (1) and (2) are true, and we can indeed keep removing one grain of sand until we have a single grain remaining. If we remove one more grain, we're left with nothing, is this still a heap?

When does the heap become a non-heap?

Workings

Hint
Look at the first and last letters.

Answer
2,300 miles.

Take the alphabetic position of the first and last letters, add them together and multiply by 100. S = 19, D = 4, 19 + 4 = 23, 23 x 100 = 2,300.