What Hot Dogs Can Teach Us About Number Theory — Quanta Magazine

My latest column for Quanta Magazine was inspired by the true story of me being frustrated by a six-pack of hot dogs.

If you’ve ever had to buy hot dogs for a cookout, you might have found yourself solving a math problem involving least common multiples. Setting aside the age-old question of why hot dogs usually come in packs of 10 while buns come in packs of eight (you can read what the National Hot Dog and Sausage Council has to say about it here), let’s stick to the math that gets our hot dogs to match our buns. A simple solution is to buy eight packs of hot dogs and 10 packs of buns, but who needs 80 hot dogs? Can you buy fewer packs and still make the numbers match?

Trying to get hot dogs and buns to match up is a simple exercise in least common multiples, but it also opens to the door to more complicated math using the Chinese Remainder Theorem, a 2,000 year old algorithm for solving systems of congruences. Learn more by reading the article, which is freely available here.