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## Food Court Number Theory

I recently met some friends for dinner in an open-air food court underneath the New York City** Highline**. Much to my surprise, some arithmetic greeted us at the door.

Since beverages could not be purchased in cash, you first had to purchase **beverage-vouchers**, which could then be exchanged for beverages. The beverage-vouchers only came in two denominations: **$1 **and **$7**.

I guess the food-court operators figured that most of their customers wouldn’t be comfortable solving stamp problems, so they were kind enough to provide some example solutions to common beverage equations.

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It’s kinda funny, actually. I was reading a related problem in a book I had that contained 1,000 assorted puzzles (many of them math or physics related), and a stamp-related problem was one of them. It was something about amusement park rides requiring special currency to enter, and each of the denominations were “economically awkward primes” (like 7 or 13; numbers that would be computationally inconvenient). I don’t actually know if the question asked for the number of ways to make, I dunno, say 50 units of currency, as that kind of problem would be a pain recursively unless you had some software to reduce the time it took to solve the problem, but it does show that apparently that kind of ridiculous modeling exists somewhere else in real life. Lol.

I still think it’d just be easier to say the juices and sodas were $3.

A common question here is, given two

computationally inconvenientnumbers (like 7 and 13), what is the largest amount youcan’tmake?For example, with 7 and 13, you can not make 6, 9, or 25.