The prolog solution is cool, but I would have solved it with a bellman ford algorithm.
An instance of the problem corresponds to a directed graph that has one node for each currency and a directed edge between every pair of distinct currencies. The weight of the edge from currency A to currency B is the value in row A, column B of the exchange data table. For instance, the weight of the EUR→JPY edge is 131.7110. We define the value of a directed simple cycle in the graph to be the product of its edge weights. For instance, the value of the USD→EUR→BTC→USD cycle is 0.7779 * 0.01125* 115.65 = 1.01209651875. An arbitrage opportunity is then a directed simple cycle with value > 1.
I was stuck here until I came across the clever trick of using the logarithm, as pointed out on http://stackoverflow.com/questions/2282427/interesting-probl...
To apply Bellman-Ford to this problem we use the negative of the base-10 logarithm of each edge instead and use the sum of these new edge weights rather than the product in calculating the value of a cycle. (Any base will do, provided we use the same base for every edge.) For instance, the weight of the EUR→JPY edge is now considered to be -log(131.7110) =~ -2.1196, and thus the weight of the USD→EUR→BTC→USD cycle is now -log(0.7779) + -log(0.01125) + -log(115.65) =~ -0.00522. An arbitrage opportunity is then a directed simple cycle with negative weight, which can easily be detected by Bellman-Ford.
What logarithm does is just a order preserving homomorphism from (R,*) to (R,+).
(I work at Priceonomics)