Triangular Number Series

It turns out that the minimum number of point to point resistance measurements that you have to make to test between all of the pins on any connector is given by something called the triangular number series. If you have only 2 pins to test, you just need to make one measurement. If you have three pins, you test from the first to the second, the first to the third, and the second to the third for three measurements. For four pins it's 6 measurements, for 5 it's 10 and so on. Each number of the series, 1, 3, 6, 10... is the previous number of the series plus the number of the next place!

Here is an online calculator for numbers in this series, although it's mostly of passing interest since it's really easy to code a triangular number calculator in any language:

http://www.mathgoodies.com/calculators/triangular-numbers.html