A few weeks ago, I blogged about a calculator giveaway at Wild About Math. Since then, Sol has posted a submitted solution here (and here’s the direct link to the pdf solution by Nate Burchell).
Here’s the problem for those who didn’t see it:
One can create a triangle of consecutive positive integers as follows:1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 . . .
Each row, R, has R numbers. Each column, C, has infinitely many numbers. Rows and columns begin at 1. We define a function F(R,C) for row R and column C such that F(R,C) gives us a value in the triangle. Thus, F(1,1) = 1, F(2,1) = 2, and F(2,2) = 3. Note that F(R,C) is only defined when 1 < = C <= R.
Part 1: Come up with a formula that computes F(R,C) in terms of R and C for any positive values of R and C when 1 < = C <= R. Show your work.
Part 2: Come up with a formula or algorithm that, given a positive integer n, determines R and C.
I also solved the problem and submitted a solution but I didn’t win. Here’s my own solution.