39

Solved in 10 moves including "Add a comment" and "Add Comment" buttons at the start and end I was muddling around in the "inspect element" for way too long trying to find something I could use in the html.


27

This is hugely inspired by @rhavelka's answer, so make sure to upvote him/her as well! Just found an alternative of where the phrases can come from:


8

Phew finally got it in 9 I believe. Took a while to find, with help from other posters (see their post for better explanation of some shared steps)


6

Let's focus on the A few observations: Conversely: This already resolves C as To avoid tedious edge cases I'll assume that the enclosure is a rectangle with one side completely open. B A


4

A cheaty one, solved in 6 moves.


4

If both players play optimally then I think that Reasoning


3

The answer is Corridor Property: Sustainance property: Starting the main plane: Retriving the refuelers: Recieving the plane: The final stretch: I apologise this is really confusing to read. I will try to make an animation soon, but I am very busy with school atm.


3

Here's how you can do this: This works with probability 1: ¹ "almost surely" is a mathematical term meaning "the probability is 100%, but there may still be possibilities that violate this". For instance, if you flip a coin infinitely many times, you will almost surely get a heads. The sequence "tails-tails-tails-..." still ...


2

After recalculating the table I believe that there is a winning strategy for A, as follows: A chooses 1 first and ends up winning by 1 point. See Tables below showing the way an optimal game could progress. Spoiler space added as I cant work out how to hide a table. An optimal game would progress as follows (Asc and Bsc are the scores for A and B after ...


1

Here is my intuition on it, which is not mathematically rigorous. Answer Explanation As stated by Hint 2, running between 2 columns of zombies can't be done infinitly as zombies get too close to us after some distance. Yet it seems a good starting point. Let's consider we get to point 50, 50 and then run upwards (between the 2 columns of zombies). We will ...


1

hexomino's answer nicely resolves the question as asked (and, Hemant, if you're in any doubt as to which answer you should accept I think it should be hexomino's). I did some computer brute-forcing which suggests a general pattern. Suppose there are $r$ rows and $c$ columns; then the final score with best play is: Let's prove this. The approach will be ...


1

I'd like to complement the other answers by a more formal explanation.


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