This post is not categorized in any of our standard categories. It has a little bit of everything, but not enough of anything to be considered part of that category.
There is an infinite plane. It has an infinite amount of leaves. There is one ‘leaf unit’ per square metre. You are raking all of these leaves. You want to find the best way to rake the leaves; there are infinitely many, so the littlest efficiency will save you an infinite amount of time. It takes you 1 time unit to move a metre with no leaves. It takes you two time units to move a metre with 10 leaf units on your rake. 3 with 20, and so on. Your rake has length 0.5 metres. That means you can pick up a leaf 25cm to your right or left without moving to it. To bag a pile of leaf units, it takes 2 time units plus 1 for every 5 leaves. A ‘pile’ of leaves must have a radius of no more than a metre. Can you figure out the most efficient plan? How many time units per leaf unit raked?