Logic/math questions from the interview

darthbob88 · Post by **darthbob88** » 2007-02-24 04:29pm

Braedley wrote:Since no one else is using the PM, I guess I won't either (dammit, I was going to get #3 )

Anyways, #1 is easy and basically solved but not posted so:

There are only two possible events where the ants will not collide. 1-if they all take the left route, 2-if they all take the right route. There are a total of 2^3=8 possibilities. 2/8=0.25=25%

Actually, Surlethe already posted that solution, with approximately the same logic.

Post by **Surlethe** » 2007-02-25 04:08pm

If anyone's interested in a bit of math trivia, really, what the ants-on-a-triangle question boils down to is, "How many non-identity maps are there from a triangle to itself that (a) are bijective and (b) preserve orientation?" The subgroup of rotations, sans the identity, is the answer.

Darth Servo · Post by **Darth Servo** » 2007-02-25 07:21pm

OK, here's a simple one. A plane takes off from South Bend Indiana at 11:30 am and lands at Chicago O'Hare intarnational airport at 11:00 am. How?

True story.

PS I will laugh at anyone who can't figure it out.

Elheru Aran · Post by **Elheru Aran** » 2007-02-25 07:35pm

Darth Servo wrote:OK, here's a simple one. A plane takes off from South Bend Indiana at 11:30 am and lands at Chicago O'Hare intarnational airport at 11:00 am. How?

True story.

PS I will laugh at anyone who can't figure it out.

Time zone. Duh.

drachefly · Post by **drachefly** » 2007-02-25 07:55pm

Surlethe wrote:If anyone's interested in a bit of math trivia, really, what the ants-on-a-triangle question boils down to is, "How many non-identity maps are there from a triangle to itself that (a) are bijective and (b) preserve orientation?" The subgroup of rotations, sans the identity, is the answer.

What's especially interesting is that the desired answers are all rotations, going all the way up to pentagons, even if they didn't need to say that it was along the edge. The ants just have to move at a fixed speed (either a constant or proportional to distance covered) to its target vertex. Hexagons are the first to require the proviso they required, and that's accomplished by breaking it up into two triangles which don't intersect, but do rotate among themselves. The first solution where ants actually cover the same ground (but at different times) is the heptagon, using the symmetry operation (145)(2367).

skotos · Post by **skotos** » 2007-02-27 09:03pm

Sorry if these questions have been answered discussed earlier, but since the thread has the rare distinction of being its own spoiler, I have skipped it in its entirety.

Pint0 Xtreme wrote:1.) There is a triangle with an ant on each vertex. Hence, three ants each on a vertex. Each ant is about to traverse on the edge of the triangle to another vertex. So each ant can choose one of two paths to traverse. What is the probability that the ants will not collide with each other?

In order to clarify this question, please answer the following: Given that each ant is facing in a given direction, and that if no ant turns before moving they will not collide, what is the probability that each ant will turn before moving?

Pint0 Xtreme wrote:2.) There is a rectangular cake. Some freeloader has cut a piece of the cake, which happens to be rectangular as well. The rectangular cut can be of any arbitrary size, in any arbitrary position and in any arbitrary orientation. With a single straight slice, how would you determine where and how to cut the cake so that you separate the cake into two equal halves?

How are we allowed to define our slice? For example, can I say, "I cut halfway along the longer side of the previous slice?" More generally, am I allowed to measure each side of the cake before cutting? To put it a different way, how am I allowed to define where my slice takes place?