Problems we’ve cared about

How many ways are there to get $1.21 using only half-dollars, quarters, dimes, nickels and pennies? (David)

There are some number of lockers, and they all start closed, and then one student goes and opens each one, and then a student toggles every second locker, and then a student toggles every third one, and so on. Toggling means that they open the locker if it’s closed and close it if it’s open. Which lockers are open in the end? (Justin)

Imagine four towns, arranged in a square.What is the minimum length of road you need to connect all of these towns? (John)

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