1. A million grains of sand is a heap.
2. If we remove one grain of sand from a heap, we 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. When does the heap become a non-heap? If we remove one more grain we're left with nothing, is this still a heap?
Fred Smith bought a used car for £4,000 and sold it to Alice for £5,000.
Fred later bought it back for £6,000 and then resold it to Alan £7,000.
Hint: Imagine Fred started with a large sum of money.
Imagine Fred started with £20,000, after buying the car he would have had £16,000. He then sold it to Alice, which left him with £21,000 and then bought it again leaving him £15,000. Fred finally sold it again leaving him with £22,000. So Fred's profit was £2,000.
Alternatively, you can see that Fred spent a total of £4,000 + £6,000 = £10,000 and received a total of £5,000 + £7,000 = £12,000. A difference of £2,000.
Below you will find 15 well-known six letter words, with only their endings remaining. Can you determine the words?