Thread: Is this a puzzle? View Single Post
 2020-08-04, 14:11 #4 kruoli     "Oliver" Sep 2017 Porta Westfalica, DE 3×5×43 Posts Brute force probability analysis. Hitting < 718K should have a probability around 1 in 2e7, so still achievable by brute force, hitting < 710K is much less likely with 1 in 8e76. Formula used (please correct me if my approach is not applicable): $p = \frac{\sum_{k=0}^{x}{\binom{\lceil log2(n) \rceil}{k}}}{n}$ $$p$$ is the probability. $$n$$ in the number we want to "depopulize". $$x$$ is the target popcount. If our target popcount would be greater than $$\lceil log2(n) \rceil$$, take the sum from $$x$$ to $$\lceil log2(n) \rceil$$. Since we are multiplying $$n$$ with another value to "depopulize" it, the final result number is getting larger. This is not displayed by this formula, but should not make a huge difference, since our value for multiplication is really small in comparison. Last fiddled with by kruoli on 2020-08-04 at 14:14 Reason: Minor clarifications.