I didn’t “just see” the answers to the questions the first time I saw them, but neither would I say that I had to solve them entirely formally. It was more like docking a boat—the river keeps tugging at the tail end, until you feel the boat’s side touch the berth and know it has stopped. There’s a kind of natural inertia to this kind of puzzles.
Also, there is a kind of problems like “one wallet contains ten coins, another one contains twice more, and the total is twenty; explain” that get asked much earlier than kids learn algebra, if I remember right. But it gets dismissed, in favour of cases where you must learn not to count the same bits of evidence twice (cough Bayes cough). I like to think this dismissal bites people in the backside when they learn Mendelian genetics (more easily seen when the genes in question interact hierarchically) or, Merlin forbid, mass-spectrometry, where the math difficulty is complicated by the chem difficulty of molecules not dividing into usual subunits.
Whew, I was thinking to write a separate post on this, but now I don’t have to! Profit!
I didn’t “just see” the answers to the questions the first time I saw them, but neither would I say that I had to solve them entirely formally. It was more like docking a boat—the river keeps tugging at the tail end, until you feel the boat’s side touch the berth and know it has stopped. There’s a kind of natural inertia to this kind of puzzles.
Also, there is a kind of problems like “one wallet contains ten coins, another one contains twice more, and the total is twenty; explain” that get asked much earlier than kids learn algebra, if I remember right. But it gets dismissed, in favour of cases where you must learn not to count the same bits of evidence twice (cough Bayes cough). I like to think this dismissal bites people in the backside when they learn Mendelian genetics (more easily seen when the genes in question interact hierarchically) or, Merlin forbid, mass-spectrometry, where the math difficulty is complicated by the chem difficulty of molecules not dividing into usual subunits.
Whew, I was thinking to write a separate post on this, but now I don’t have to! Profit!