Big Online Courses Have a Problem. Here’s How We Tried to Fix It.

The Problem Here is some personal prejudice: I don’t love online courses. I
love learning in community, even in online communities, but online courses
rare...
4 weeks ago
The answer is 24800.
ReplyDeleteInteger solutions correspond to lattice points inside the right triangle with vertices (0,0), (250,0), and (0,200), together with the points on the hypotenuse, but excluding (250,0) and (0,200).
We start with the rectangle with corners (0,0), (250,0), (0,200), and (250,200). The rectangle contains 251*201 = 50451 lattice points.
The diagonal from (250,0) to (0,200) contains 51 lattice points. Of the remaining 50400 lattice points, half of them (or 25200) lie below the diagonal.
To get the final answer, we add back the lattice points on the diagonal, and then subtract the lattice points on the axes.
So the answer is 25200 + 51  200  250  1 = 24800.
;; Brute forced in scheme:
ReplyDelete(define (potd x c) (if (> 1001 (* 5 x)) (potd (+ 1 x) (+ c (floor (/ ( 1000 (* 5 x)) 4)))) c))
(potd 1 0)