Pegs and Holes, Part I

WARNING: If you have any shred of doubt left that I, Josh Allen, am not a dork, please discontinue reading my blog immediately.

As I so often do in order to spice up the work day a bit, I had a little debate with my co-workers earlier today. As we were defining a problem with a software application we're developing, I uttered one of those archaic idioms common to the English language: "It's like trying to fit a round peg in a square hole." My co-worker responded, "You mean 'a square peg in a round hole.'" It went on like this for a little bit... I could've sworn the former was the customary way to express this adage.

But, no, it didn't stop there. He told me authoritatively, "But you can fit a round peg in a square hole!" To which those nerdy-sounding alarm bells related to the part of my brain that made me become a math minor rang resoundingly. I repudiated that falsehood (or at least what I was moderately confident was a falsehood), and we consluted Co-Worker #2. He sort of agreed with both of us, not really able to decide.

But we dissected the situation even further. I insisted that, given the appropriate size, you could in fact fit a round peg into a square hole (if the peg is much smaller than the hole), and vice-versa. But, if they were the same size, you couldn't fit a round peg into a square hole OR a square peg into a round hole. So actually, I proclaimed, the idiom has the same meaning in both of its variations. Co-Worker #1 stubbornly maintained that, even if the peg and hole are the same size, the round peg would fit.

We left the topic alone for the day (argh, finally!), because we actually had lots of other important things to do (like, oh, a little 30-page business plan complete with scientific rationale of our product, etc., etc., all due at 5pm Tuesday). But, like a good little math minor, I did find out the answer AND proved it. My question to you (assuming you haven't collapsed in utter boredom or left for something more interesting like, say, C-SPAN 3): Who's right? Solution tomorrow.