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## Hot Dog Bun Math

It’s the 4th of July weekend here in the US. Today’s BBQ1 got me thinking about that conspiracy theory from Father of the Bride regarding the mismatch of hot dogs quantities and hot dog bun quantities. Steve Martin’s character goes nuts over the discrepancy.

This is really an exercise in Least Common Multiples that no teacher seems to exploit (at least none that I ever had).

Research tells me that the reality of this joke is a little more complicated than 8 hot dogs and 12 buns. It may even vary based on location. From what I can tell the most common hot dog packages are 8 and 10, while the most common bun packages are 10 and 12. That means a 10/10 purchase is a win in terms of efficiency. I suspect there are more combinations, but 8/10 and 10/12 seem to be the most common. Here’s a table of the possibilities:

Hot Dog Qty. Hot Dog Bun Qty. Least Common Multiple Least Hot Dog Packages Least Hot Dog Bun Packages
8 10 40 5 4
8 12 24 4 2
10 10 10 1 1
10 12 60 6 5

This leaves me to question: who profits more from this? To figure this out, we’d need to know buying habits of people and costs involved in producing, packaging, shipping these goods. I don’t have that on hand, but I can draw a pretty graph of how many packages of each you’d need to not waste food:

So it looks like we’ll be eating hot dogs in sandwich bread and making tiny sandwiches out of left over hot dog buns for years to come.

1. Technically you grill hot dogs (hot and fast), not BBQ (low and slow) but American etymology is funny.