The Sheriff’s Star: Arithmetic Solution
If you haven’t already read the problem description for the Sheriff’s Star, you might want to do that before looking at solutions.
The arithmetic solution doesn’t use anything beyond division, and so it’s theoretically fine for 1849 gold miners. It would be tedious to do some of these calculations by hand (I’d use a calculator), but it can be done.
My mom (Karen Butler Easter) was the first one to present this solution to me; I didn’t find it on my own. She’s an excellent lateral thinker, and it shows in this solution: straightforward and lovely.
Start by marking a center point and then use the string (acting as a radius) with a pencil at the end of it. Mark out a circle. (You could also probably do this with a compass or a pair of dividers—it seems likely that a goldsmith might have both.)
We could certainly calculate circumference based on some numeric methods here, but it’s easy just to measure it, and that’s likely to be precise enough for our goldsmith. So we measure it with the string, marking the string to show the total length.
Then we go back to mark the string up with equally-spaced points. If you have a calculator, you can do this by multiplication or by repeated addition; if not, you might just mark the length of x on a piece of paper and use that repeatedly to mark each segment.
This approach is similar to one that’s frequently used for laying out repeated measurements in woodworking: a story pole or scantillion.
There you go! Simple, easy, and not much calculation involved. Head back to the Sheriff’s Star page to see links to other solutions people have created.
Have you come up with a new solution? Leave a comment!