The Math
Bruteforcing is finding the fastest path between elements and then doing attempts with the hope of getting wanted order. "n-element map" is simply a map with n number of elements (Countries, Continents, Counties, States, etc). n - number of elements to click on m - number of attempts p - the probability of succeeding These formulas help to calculate:
What is the probability of succeeding in the n-element map after m attempts?
1-(1-(1/(n!)))^m = p
How many attempts are needed to have a certain probability p of succeeding on the n-element map?
log(1-p)/log(1-(1/(n!))) = m
As doing these operations is quite complicated and/or nearly impossible for human, I recommend using: https://www.mathsisfun.com/calculator-precision.html (for the first formula) or https://www.wolframalpha.com/ (for both)
Here's a simple calculator made by @saifo https://www.calconic.com/calculator-widgets/brute-force-percent-change-calculator/62508c2a25b5a3001f08357f?layouts=true
Examples
We want to calculate a probability of getting 7-element map after 1000 attempts: 1-(1-(1/(7!)))^1000 = 18.00%
now after 2000 attempts: 1-(1-(1/(7!)))^2000 = 32.76%
Now we want to calculate the number of attempts needed to have a 50% chance of getting the 6-element map: log(1-0.5)/log(1-(1/(6!))) = ~499 attempts
Now for 8-element map: log(1-0.5)/log(1-(1/(8!))) = ~27 947 attempts
Hello everyone,
As of now, the leaderboards are officially open for submissions. Remember to turn on speedrun mode to get the exact time with milliseconds for runs.
The other leaderboards for desktop app and mobile app will be open at a later date.
Thank you for your patience,
Darrel69