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2016/05/31 ...Some time ago a friend of mine, Adam Atkinson, mentioned to me what he referred to as "Semi-Chestnuts" - puzzles that should be classics, but are for some reason effectively unknown. Recently one of these caught the attention of the Twitter-verse. I've changed it a little here for the purposes of opening the discussion - this is specifically not the version Adam gave me, and is not the version I tweeted - but it is a good place to start the discussion.
So the (modified) puzzle is:
When presented with that question, as phrased there, there are two initial reactions. One is to say that it's impossible, because a prime can never be a product. But the other is to start asking for clarification.
Until recently when I've been giving puzzles I've always answered those questions, but the responses from @DrBreitmaul brought me up short. He didn't solve the puzzle as I expected it to be. Well, actually he did, but he went much further.
You see, he asked each of those questions, and then proceeded to solve the puzzle for each of the possible answers. Instead of just taking one branch in the tree of possibilities, he investigated all of them. And the results were fascinating.
So here is a puzzle:
Now, ask a clarifying question:
Then suppose the answer is yes, you are restricted to whole numbers. Now are there any solutions? How many different solutions can you find? Is there a structure to all of the solutions? How do you know you've found them all?
And so on. So there's a whole new meta-puzzle:
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