by crispybits on Sat Mar 16, 2013 1:14 pm
Yeah it's actually fairly easy to get this until we get to either primes or ridiculoulsy high numbers.
A couple of others that I haven't seen used yet:
5# = 30 (n# is the product of all prime numbers up to and including n)
5$ = 34560 (n$ is the superfactorial, so it's 1! x 2! x 3! x .... x n!) - this one is not so useful on 5, but ⌈√5!!⌉$ (4$) = 288, and ⌈√5⌉$ (3$) = 12
A really boring version but also a bigger challenge would be to see how high we can go only using one 5, so for instance here is the five 5s way for the next one:
207 = (Γ5 + Γ5 + Γ5 - ⌈√5⌉) x ⌈√5⌉
207 = (24 + 24 + 24 - 3) x 3
207 = 69 x 3
207 = 207
But, we could also do:
207 = ⌊√√√√√√√⌈√√√⌊√√√√⌈√√√√√⌈√√√⌈√√⌈√√⌈√√√⌊√5!⌋!⌉!⌉!⌉!!⌉!⌉!!⌋!⌉!!⌋
207 = ⌊√√√√√√√⌈√√√⌊√√√√⌈√√√√√⌈√√√⌈√√⌈√√⌈√√√10!⌉!⌉!⌉!!⌉!⌉!!⌋!⌉!!⌋
207 = ⌊√√√√√√√⌈√√√⌊√√√√⌈√√√√√⌈√√√⌈√√⌈√√7!⌉!⌉!!⌉!⌉!!⌋!⌉!!⌋
207 = ⌊√√√√√√√⌈√√√⌊√√√√⌈√√√√√⌈√√√⌈√√9!⌉!!⌉!⌉!!⌋!⌉!!⌋
207 = ⌊√√√√√√√⌈√√√⌊√√√√⌈√√√√√⌈√√√25!!⌉!⌉!!⌋!⌉!!⌋
207 = ⌊√√√√√√√⌈√√√⌊√√√√⌈√√√√√41!⌉!!⌋!⌉!!⌋
207 = ⌊√√√√√√√⌈√√√⌊√√√√36!!⌋!⌉!!⌋
207 = ⌊√√√√√√√⌈√√√21!⌉!!⌋
207 = ⌊√√√√√√√291!!⌋
207 = 207
(and yes, I did have to use a spreadsheet to get there with a huge table of multiple roots to bounce around)