I'm thinking of taking a Mensa test. There's one in my home town in a couple of weeks. I've always felt that it's kind of silly to take tests no-one's making you take just to prove that you're smart or whatever, but now I'm sorely tempted
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The kind of problems you are describing are identical to mine and they all have one thing in common: they require you to use two quite different modes of reasoning and combine them with a visualisation of just one of them.
When I was 16 I could do trig, calculus etc etc. But give me a problem that started "If John has eight apples..." and I would become, in turn, baffled, stressed and finally tearful.
Edit: and I am now in charge of a huge budget, and thank god the finance officer is supportive because I cannot learn how to do this unless I figure it out for myself.
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