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 Gotchas Puzzle 13 Can you circle exactly three numbers to make a total of 19? [Ref: ZLBV] © Kevin Stone  Hint: There is a little trick to this puzzle. Answer: 12 + 6 + 1 = 19. Note that the puzzle didn't ask for three digits to be circled! Puzzle 14 What is it that the person who makes it doesn't need it. The person who buys it does not need it for themselves and the person who uses it doesn't know it? [Ref: ZZRT]   Hint: Hopefully you won't need one for a very long time. Answer: A coffin. Puzzle 15 Half of zero is still zero. What other number can be halved to make zero? [Ref: ZBQV]   Hint: This can't be an actual sum, so what could it be? Answer: Eight. When written as a digit, 8, the top half is 0, and the bottom half is also 0. Puzzle 16 How many grains of sand do you need until you have a heap of sand? [Ref: ZMQO]   Hint: Is a million grains of sand a heap? Answer: We can safely say two things: 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?