Preferably, I'm looking to demonstrate that there are problems that only mathematics can solve, even if they're phrased in another language.
Basically, it should appear that the problem can be solved with a linguistic logical approach, but ultimately only be solved using a mathematical approach.
the one apple one doesn't work because it obviously can't be done without mathematics, that should be the subtlety. As for the steep ramp arguement, the reason it was a good question is it can be modified to be something like...
What shape ramp should I make to ensure that a ball on it will always reach the bottom after the same amount time no matter where I let it go from?
(This may be too complicated as it leads to lots of vector calculations to show it's a cycloid... there's those cycloids again!)
How steep should my ramp be if I want it travelling as fast as possible after it leaves the ramp?
A question that can be rephrased like this but not mentioning numbers. Or obviously referring to needing mathematics. I want a question that I can convince someone that they can answer without maths, then show that they need maths to solve it.
I understand I'm asking a very vague question, but it's a little project I've got going, so sorry about the ambiguity.
That's a good one too, can be adapted.
But the problem with 'how much'/'how many' questions is they instantly suggest a number will be required.
But a rephrase could be something along the lines of...
Is there enough energy stored in a single atom of Hydrogen to escape the Earths atmosphere?
Though that too isn't really subtle enough.
Despite how it looks, it doesn't have to be a physics question either, anything that suggests it can be solved without maths (but in fact can't be) will do.
Asymmetrical big bang? That's the only theory I think of as doing the job.
(Big bang went out as a dumbell shape, like two balls touching, with a ring floating between them.) The ring held equal amounts while the two balls each held matter or anti-matter.