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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 nonheap? If we remove one more grain we're left with nothing, is this still a heap?
Puzzle 394
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.
Answer: £2,000.
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.
Puzzle 395
Below you will find 15 wellknown six letter words, with only their endings remaining. Can you determine the words?
During the recent BrainBashers cipher convention, a binary code contest took place.
The contest consisted of a binary code transmission where the spaces between the letters were missing and there was no punctuation.
Each letter of the alphabet was translated into its binary equivalent based on its position in the alphabet. The resulting code was then blocked in groups of five digits.
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