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Arithmetic was my bugbear in my school years.
I could somehow manage addition but not subtraction..."carrying" was easy but not "borrowing"...
When during my university years in Vizagh I went to Maitrani Brothers and bought a shirt-cum-pant combo, the bill came to Rs 82.
When I gave the cashier an awesome 100 rupee note, he quickly counted 1,2,3...18 ten rupee notes and returned them to me.
I wondered how great he was at subtraction; till I discovered that he was actually counting 83,84,85...100.
He was converting subtraction into addition :)
And if he didn't have enough ten rupee notes he would ask me to hand him an additional two rupee note!
To my wonderment he would then return me a brand new twenty rupee note :)
My HM father who was teaching our science (in addition to English) exhibited once a cute demo: it showed that we don't make our effort to breath in air into our lungs, but only to create a vacuum around our lungs...air flows in automatically!
An exhaust fan is quite the cute obverse of a ceiling fan.
There was a crazy discussion of room-heating in an obscure edition of Zemansky's Thermodynamics: instead of passing steam or hot air in pipes laid inside the room, the reverse way was to install a refrigerator in the window backside front...trying to cool the outside air :)
Our first physics lesson in college was a demo of Vernier Calipers whose theory was never taught to us. Its vernier divisions were smaller than its main divisions. Much later at KGP, I saw a negative-reading calipers whose vernier divisions were perversely LARGER than its main divisions. That forced me to use my virgin brain to figure out the theory of Vernier Calipers!
There is this hilarious story "Sale" by Guy de Maupassant in which a pig breeder wants money and a wine seller wants a wife.
The pig breeder agrees to sell his wife by volume (like his pigs)...so many francs per liter. He makes his wife fill up his drum with water; and drowns her in it. And releases her.
And says all he has to do is to measure the volume of the water that flowed away.
Wine seller asks: "How?"
"Just refill the drum again and count the number of pails of water needed!"
That is called the "Displacement Method" in our glorious physics.
Archimedes who ran naked calling "Eureka" was no better...he measured the weight LOST :)
At our student labs in our university we quickly became experts in what we called "back-calculation".
Suppose we had to measure the wavelength of sodium light using Newtons rings. If we were honest, we would get like 6100 or 5800 instead of the correct 5893.
So we use the formula backwards and calculate the radius of curvature of the lens needed, to cleverly get a passable 6000 (not precisely 5893 :)
Newton did the same with his inverse square law: he measured the time taken by his apple to fall down, inserted the known time period of the moon around the earth, and found that gravity should go inverse square (and not cube ;)
Einstein did the same with his special relativity.
Lorentz, Fitzgerald, Poincare and other stalwarts too did that back-calculation and got the correct length contraction and time dilation but they were not bold enough, being too old and hidebound.; and were dilly-dallying.
Since young Einstein didn't have any such inhibitions he boldly announced that their back-calculations described Nature precisely.
And he did something similar with his celebrated tensor theory of gravity: he made it VANISH watching a kid diving into water in free-fall.
"Atom Bomb" makers at Los Alamos did something similar: they had to extract a rare isotope of uranium occurring 7 parts in 1000 mixed with its richer isotope.
Instead of extracting the rarer one, they pumped out the unwanted richer one...using diffusion, centrifuges or whatever!
In our Hindu spiritual quest there is a way called "Jnana Marga".
In this you DON'T search for the ultimate Truth...instead, you discard obvious untruths one by one saying "not this, not this" (neti, neti).
And what survives is the Truth :)
There is this famous mantra in the oldest Ishopanishad:
హిరణ్మయేన పాత్రేణ
సత్యస్యాపిహితం ముఖం
తత్ త్వం పూషన్ అపావృణు
సత్య ధర్మాయ ద్రష్టయే
The face of Truth
Is covered by a golden disk
Unveil it Pooshan!
So I can have a peek at it
Good Day!
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