For more than a month now Oliver and I have been walking to Birchwood Intermediate School every morning just past 8 o’clock. The old walk up Prince Street to Prince Street Elementary was simple: we walked up Prince Street. Birchwood is northeast of our house, though, and so there are a seemingly infinite ways of getting there.
Actually, it turns out that there are 30 ways.
I figured this out using something called Pascal’s triangle. Here’s a simplified version of the street grid that covers the ground between the corner of Prince and Grafton (home) and the corner of Birchwood and Longworth (school) overlaid with the Pascal’s triangle’s binomial coefficients.
It took me a while to get my atrophied brain to understand Pascal’s triangle: this tutorial helped as did this animated GIF from Wikipedia:
This explanation sums it up well:
The first and last entry in each row of Pascal’s triangle is a 1. Every other entry in Pascal’s triangle is the sum of the two entries in the preceding row that lie to the immediate left and right.
So, in other words, we could go Prince-Kent-Hillsborough-Fitzroy-Weymouth-Longworth, or we could go Prince-Euston-Longworth, or we could go Grafton-Cumberland, or we could go Grafton-Hillsborough-Euston-Longworth. Total up the number of possible routes and the total is 30.
If we happened to take any of the 10 routes that pass through the corner of Longworth and Euston, we pass by a Maritime Electric pole in front of 27 Longworth that, for the first few weeks we walked by, looked like this:
I’m a tall guy and that guy wire, often hard to see in the morning sun, was positioned at the right height to catch my head if walking 2-by-2 with Oliver.
But problems have solutions, we tell Oliver.
And so I wrote a quick email to Kim Griffin, personable and award-winning “Manager, Corporate Communications & Public Affairs” at Maritime Electric. She was quick to reply – on a Sunday, no less – and by Monday morning the guy wire had been tightened up and shrouded in a protective and easy-to-see yellow shroud.
Many lessons learned.