Random Puzzles 

Workings

Hint
The words are all vegetables.

Answer
Caehikort, which is an anagram of artichoke.

The others all begin with the letter C: celery, carrot, cabbage, and cauliflower.

Workings

Hint
One of the cheeses is Cheddar.

Answer
Edam, Cheddar, Brie, Cheshire.

Workings

Hint
How much of a warren can each rabbit dig in one hour?

Answer
2 hours.

Reasoning
The small rabbit can dig a warren in nine hours, so digs ¹⁄₉ in one hour.

The medium rabbit can dig a warren in 6 hours, so digs ¹⁄₆ in one hour.

The large rabbit can dig a warren in four and a half hours, so digs ¹⁄_4.5 in one hour.

   1 Hour = ¹⁄₉ + ¹⁄₆ + ¹⁄_4.5

To make the denominators all the same, we can multiply through by ¹⁸⁄₁₈ to give:

   1 Hour = ²⁄₁₈ + ³⁄₁₈ + ⁴⁄₁₈

   1 Hour = ⁹⁄₁₈

   1 Hour = ¹⁄₂

So in one hour, they have dug half a warren, the whole warren will therefore take 2 hours.

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?