652 karma · joined May 10, 2012
using Combinatorics
# Initialization
numbers = [1, 2, 3, 4, 5, 6, 7, 8, 9]
primes = [3, 5, 7, 11, 13, 17]
winners = []
# Loop though the permutations, collecting only prime pairs
for p in permutations(numbers)
for i in 2:9
if !(p[i-1] + p[i] in primes)
@goto nextpermutation
end
end
push!(winners, p)
@label nextpermutation
end
If I were to use a non-brute force approach I would consider computing all the hamiltonian paths of a graph where each vertex is a number and two vertices are connected only if their sum is a prime number- Bigger screen would be great for my use case
- Software. As have been said repeatedly here the tablet is open. This is true in the sense that in order to comply with the GPL3 it's very easy to SSH to the tablet which runs Linux. This is awesome. However I think a little more support to developers would be great in the form of documentation instead of reverse engineering. Lot's of people think of ways of improving the software and this would make it much easier and better for end users (for example better file transfer, more file formats... in a reliable way)
Edit: formatting
Edit: typo
"We ran all three experiments simultaneously on 20 nodes on the Lonestar5 cluster and computing on 24 CPUs per node in parallel."
It seems it took less than an hour. I think that calling it a "fleet of computers" is a little too much. It makes it look like they brute-forced the problem while the truth is that as usually the merit was on the algorithm.
If you think a shorter elegant proof is more desirable, well, I totally agree with you. I think math is more about the proofs than the results. On the other hand I have zero problems trusting a proof checked by a computer. I don't know you but I usually trust much more computers with tedious computations than myself.
I doubt proprietary tech is going to fade completely, but it's true that maybe there are forces that are pushing for big companies to make more and more projects open source. If you think about it it makes sense: the employees are happier because their work has more impact, they also benefit because they can showcase it in their CV. For the company they externalize testing, quality improves because employees are going to be more careful when their code is in the open and they are more motivated. It can also make hiring easier.
"If first player has a K, because of 1. and 2., he would only lose if he bets. So first player should pass if he has a K."
It actually means that the first player always loses on average if he bets (expected utility -1/2 if not mistaken). If he folds however the expected utility is clearly zero since half of the time wins and half of the time loses.
I have not reached yet the description of the algorithm.
I actually find somewhat paradoxical that the first player should fold with a K and bluff with a Q! I remember that I loved little results like this when years ago I first followed the game theory course in Coursera. It was a little dry but I completed it nevertheless since I found it quite fascinating. I do wonder what possible applications are for my working field, machine learning, to apply these kind of algorithms. I would love to have an excuse to devote some time to it.