Maybe just me, but that problem does not look very simple at all. One reason OP's problem is appealing, is because the solution can be easily checked. The solution is a kind of "proof of work". You could never guess the solution without a deep understanding of the problem. But once found, the solution is immediately verifiable.
For many problems one can easily guess the solution, without necessarily knowing the proof (like Fermat did). The answer is almost certainly negative, and a complete solution requires a very long and tedious proof that cannot be checked without a deep understanding of the field and many years of collective effort.
I am specifically interested in problems which can be understood by a child, have hard solutions which cannot be easily guessed, but are easily verified (ex. factoring the product of two large primes). It seems like these problems would make good candidates for one-way-functions, like the diophantine equations and ECC. But elliptic curve cryptology is too difficult to describe to a child.
Quite easy to explain given a few graphs. The explanation boils down on how hard is to accurately draw a curve of such an elliptic function at big x (P3) and then figure out which two other points intersect with a given line near. You can even show it on a big whiteboard.
You can even show how easy out would be for a simple curve where the left part is an easy equation.
The hard part is what makes an equation easy to solve. (And how some elliptic are broken.) It takes at least some high school math to hint at this.
For many problems one can easily guess the solution, without necessarily knowing the proof (like Fermat did). The answer is almost certainly negative, and a complete solution requires a very long and tedious proof that cannot be checked without a deep understanding of the field and many years of collective effort.
I am specifically interested in problems which can be understood by a child, have hard solutions which cannot be easily guessed, but are easily verified (ex. factoring the product of two large primes). It seems like these problems would make good candidates for one-way-functions, like the diophantine equations and ECC. But elliptic curve cryptology is too difficult to describe to a child.