If you would allow ceiling function then I could give you a solution with score 60 for the Puzzle 1. Ceiling or floor functions are cool because they add even more branches to the search, and enable involving irrational number computations too. :P Though you might want to restrict the number of ceiling or floor functions permitted per solution.
By the way, please share a hint about how do you enter spoilers here?
Yes, maybe the the minimum cost is 3 even without floor or ceiling? But the question is then how to find concrete solutions that can be proven using realistic efforts. I interpret the challenge as request for submission of concrete solutions, not just theoretical ones. Anyway, my finding is below, maybe it can be improved further. And could there be any way to emulate floor or ceiling using the functions permitted in the initial problem formulation?
By the way, for me the >! works reliably when entered right in the beginning of the message. After a newline it does not work reliably.
If you would allow ceiling function then I could give you a solution with score 60 for the Puzzle 1. Ceiling or floor functions are cool because they add even more branches to the search, and enable involving irrational number computations too. :P Though you might want to restrict the number of ceiling or floor functions permitted per solution.
By the way, please share a hint about how do you enter spoilers here?
Typing >! at the start of a line makes a spoiler
I conjecture you can get every positive integer with cost 3 and a single floor function, but it also seems very hard to prove.
Yes, maybe the the minimum cost is 3 even without floor or ceiling? But the question is then how to find concrete solutions that can be proven using realistic efforts. I interpret the challenge as request for submission of concrete solutions, not just theoretical ones. Anyway, my finding is below, maybe it can be improved further. And could there be any way to emulate floor or ceiling using the functions permitted in the initial problem formulation?
By the way, for me the >! works reliably when entered right in the beginning of the message. After a newline it does not work reliably.
ceil(3!! * sqrt(sqrt(5! / 2 + 2)))