Problems & Puzzles: Puzzles
Puzzle 277. Pi again
Cino Hilliard sent the following claim related to an old puzzle of these pages:
The claim is not true according to the rules of the Puzzle 50 (in order to calculate the rank associated to a solution we take into account only the good decimal digits of the approximation to Pi).
The real rank of the Cino's solution is (11/12)*100 = 91.6...%.
Nevertheless this rank is the highest rank already obtained for the Puzzle 50 by the simple quotient of two primes!
Apparently Cino's has found a systematic approach in order to get good approximations and in his email he challenges us to find what his method can be.
1. Can you get a better solution than the Cino's one using only the quotient of two primes and a systematic approach?
Adam Stinchcombe wrote:
Interesting the Stinchcombe's guess about the Cino's method. Regarding the quotient calculated by Adam is interesting too, but not yet I will remove the requirement of the current puzzle. I still think that a better quotient could come soon.
Nevertheless I don't remove the requirement to this puzzle, I want to report my 'best' result trying to hunt a better result than the Cino's one:
2795342701/889785217 = (7727 * 361763)/(277 * 383 * 8387) = 3.14159265358979323 Rank = 17/20 = 0.85
Form the result reported it's evident what was my approach. Anyway, no better result in any sense. Sorry.