Brainripples

Thanks for all the thoughts on my little math problem. (And, yes, I knew that 85 was a good an answer as 80; in this case I decided to use "distance to the middle of the range" as a tie-breaker.)

As some of you might have guessed from the number 2,711, the diagram that I was writing a script to generate is the current status of the Dafcast database: each square is one page, marked green for translated and orange for "in progress". White boundaries group pages into tractates.

It's actually a quite effective visualization. And once we have some history, it will be interesting to animate it. (We'll also have some additional states soon, like "edited", "scripted", "recorded", and "released".)

Here's a math problem I've been struggling with. Well, I've been struggling with its practical application, and I'm going to write an Excel spreadsheet to solve it by brute force, but I wonder if it would fall to an elegant algorithm.

Given a number N and two smaller numbers a and b, find x such that x ∊ [a, b] and N mod x is maximized.

(Practical application: Given 2,711 squares, each color-coded to indicate the status of one member of a sequence, arrange them in a rectangle whose width is between 70 and 90 such that there are the fewest number of unused squares in the lower right-corner. Excel tells me that the answer is width 80, which has 9 leftover squares.)