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MixedNuts comments on Two barrels problem from the Intuitive Explanation (answered) - Less Wrong
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This reminds me of those tests in grade school that tell you to read all the instructions before starting, then to do all kinds of silly stuff, then to ignore previous instructions. I wonder if careful reading is good for things other than not getting tricked by such jokes. (And accidental instantiations thereof on written tests.)
There are a few other cases I can think of offhand where careful reading is important. Decoding poorly written instructions and this card game in particular came to mind immediately, but on reflection I think the best example in my experience would be coding, and in particular debugging. I'm by no means an expert (or necessarily a representative sample), but at least half of the bugs I spend 10+ minutes chasing around end up being caused by a minor brain-dead error in a single expression.