Answer to Wild About Math Giveaway Problem

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:

 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.


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