Aha! Insight

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1. dfanJan 2023
   This is different from the other answers, but it does answer your question: When I was a kid I had tons of math and logic puzzle books. Two I remember specifically are "Aha! Insight" and "Aha! Gotcha" by Martin Gardner. Decades later, when a math problem comes up in my work, I have an apparently unusual ability to cut to the heart of it ("by symmetry, we must have X" or "looking at this extreme case, we must have Y" or "this looks like a special case of Z" sort of things) instead of starting by soldiering through equations, and I credit a lot of that to all the puzzle-solving I did as a kid.
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2. supernova87aJan 2022
   Actually both books, but I was particularly thinking first of the "Aha Insight!" book, which has like 100 different problems where some clever thinking/turning around the problem statement helps to solve it.

   The other one ("Aha Gotcha"), you are right is more about paradoxes that arise when applying logic that seems to lead to contradictory outcomes. But it also has a lot of "change the way of thinking" answers.

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3. savanalyOct 2015
   My favorite books by Gardner, and these are great introductions to his lighthearted approach to math, are the pair Aha! Insight [1] and Aha! Gotcha. These are probably the least rigorous works he made, but extremely fun and still tackle interesting subjects (in other words, great for kids). If you want something longer form or less approachable, he was a very prolific author so any of his other dozens of books are great too.

   [1] http://www.amazon.com/Aha-Insight-Martin-Gardner/dp/07167101...

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4. zcarterOct 2014
   If anyone is looking for a starting point to Gardner's vast works, I highly recommend "Aha! Insight."
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5. dvgrnNov 2022
   The reference that comes to mind for me is something out of one of Martin Gardner's _Aha! Insight_ books from decades ago -- the idea of encoding something like the Encyclopedia Britannica into one big long bitstring, then converting it into a fraction... and putting one single very careful mark on a stick to represent that fraction.

   The difference is that where the real world doesn't allow for storing anywhere near that level of precision in a mark on a stick, the Conway's Life universe is considered to be unbounded, so there's as much room as we need to implement this RCT trick.

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6. lern_too_spelJan 2015
   Your friend read Martin Gardner's aha! Insight, which has exactly this proof in it and is a popular book for young mathematical puzzle enthusiasts.
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