thought of xoxo immediately

(http://www.autoadmit.com/thread.php?thread_id=3809798&forum_id=2#34840879)

The n-mig problem: how many failures are possible in mig's life when time t=n

(http://www.autoadmit.com/thread.php?thread_id=3809798&forum_id=2#34778135)

https://s3.amazonaws.com/codechef_shared/download/Solutions/2011/November/DOMNOCUT.pdf

i see now what they are asking for and think that i can find a solution for smaller n & m values....aka brute force :-p

im going to think more about what dimensions would force you to add more colors...very cool brother

(http://www.autoadmit.com/thread.php?thread_id=3809798&forum_id=2#34840819)

you're allowed to incorporate non-facial features like Adam's apples

(http://www.autoadmit.com/thread.php?thread_id=3809798&forum_id=2#34840902)

if you have a circle of matter, and it exploded in such a way that every atom went flying from every conceivable start point, at a trajectory with a constant slope...it would not cover the universe? right?

you need things with different slopes i think this is a another cool problem i will think on

(http://www.autoadmit.com/thread.php?thread_id=3809798&forum_id=2#34841038)

Computational problems are always discrete. Assume the spaceship can only occupy cells in a 3D grid.

(http://www.autoadmit.com/thread.php?thread_id=3809798&forum_id=2#34841069)

edit i was typing after u had already poasted fma

(http://www.autoadmit.com/thread.php?thread_id=3809798&forum_id=2#34841092)

Do I need to blow it up in finite time?

(http://www.autoadmit.com/thread.php?thread_id=3809798&forum_id=2#34841042)

Assume the spaceship can only be located at discrete locations in a 3D grid.

(http://www.autoadmit.com/thread.php?thread_id=3809798&forum_id=2#34841078)

Say you're in a 3D grid and the spaceship is a grid square. Traverse the X-Y plane in a spiral outward from the origin, firing torpedos up and down in the Z direction at each step.

What's wrong with this trivial solution?

(http://www.autoadmit.com/thread.php?thread_id=3809798&forum_id=2#34841109)

Now do the same while the spaceship is moving at a constant velocity along one dimension.

(http://www.autoadmit.com/thread.php?thread_id=3809798&forum_id=2#34841151)

Are the torpedos faster than the target?

(http://www.autoadmit.com/thread.php?thread_id=3809798&forum_id=2#34841193)

The torpedoes are infinitely fast but you can only fire one per time step.

(http://www.autoadmit.com/thread.php?thread_id=3809798&forum_id=2#34841217)

To each square in the grid, attach a copy of Z^3 representing all possible discrete velocity vectors. There will be duplicates but this doesn't matter.

Together we have a countable set and it's not hard to enumerate it. Walk through this enumeration at each time step. You will eventually land on a grid cube lined up with the ship AND the right movement vector. Then your infinitely fast torpedo kills it.

(http://www.autoadmit.com/thread.php?thread_id=3809798&forum_id=2#34841294)

edit: even if you allow for a +-1 velocity along each axis rather than only one axis and direction, there are still finitely many possible initial velocity vectors, so you still have a countable set of possibilities for where the spaceship is at time t for each initial velocity combination

(http://www.autoadmit.com/thread.php?thread_id=3809798&forum_id=2#34841190)

You are on the right track but your search algorithm seems a little hazy. How do you avoid visiting the same location-velocity cell twice?

(http://www.autoadmit.com/thread.php?thread_id=3809798&forum_id=2#34841247)

even given that the velocity can be N cells per time unit it's still true that a countable union of countable sets is countable so there is a way to thread together an infinite parallel search of all possible initial velocities plus initial positions by shooting at the current calculated position, but tbh i have to think more about never shooting the same position more than once.

(http://www.autoadmit.com/thread.php?thread_id=3809798&forum_id=2#34841268)

edit: in more detail, there are countably many initial position vectors which are elements of Z^n for however many spatial dimensions there are, and countably many initial velocity vectors which also live in Z^n. The total phase spae is Z^n x Z^n which is also countable, so you can find a way to shoot one by one at the current position of each possible (initial position, initial velocity) pair.

assume we're in 2D. if you start at (x0, y0) with velocity (vx, vy) then at time t you are at (x0 + t * vx, y0 + t * vy). go through all possible initial conditions (x0, y0, vx, vy) and shoot at the predicted location at whatever time index you assign to the point.

(http://www.autoadmit.com/thread.php?thread_id=3809798&forum_id=2#34841297)