From time to time, I’m going to add websites or problems that I think challenge visitors in rich ways. One of my very favorites is a little wonder called “Petals around the rose”. There is a nice implementation by Lloyd Barrett on his website. Prepare to spend some time on this, and don’t bother going if you’d ever contemplate doing a web search for solutions. If it takes you a week to solve, it’s a well-spent week. It took me several days (so no, I don’t want to hear about it if you solve it simply after visual inspections 🙂 ). There are several problem solving aspects that I think make this a rich experience… [No spoilers below]
I’m giving nothing away to point out that there is a numerical approach. One unique aspect is that you cannot design your experiment–you simply request more data, and are shown some. If you’re looking for input about what a certain collection of dice would output, you’ve got to wait for it, and to seek for information in whatever patterns come to you. This certainly resembles many branches of science–not so much the molecular biology approach, but some aspects of cell biology and many of evolutionary bio or ecology.
Some of my own fascination arose because of my individual path. I got to a partial solution in relatively good time, but some of the aspects of the inner workings actually meant the problem was harder to solve from that position, because what I knew colored what I saw.
A second aspect that I really like is that there are two largely independent paths to the solution. One is to focus solely on the mathematical element. However, it’s important to point out that the name (Petals around the Rose) is a meaningful clue. When I have assigned this in class, I have sometimes told pairs that one member should explore hypotheses about the name; the other about the mathematical patterns.
When delivering it, I’ve tried to make the process metacognitive by requiring students to keep track of their hypotheses and the data that destroyed them. What I’ve learned is that instructions and requirements need to be rigorous here, or you don’t get much back. Alas, I’ve not developed these, but keep an eye out here. While it’s very difficult to convince modern students to take such an approach, this problem lends itself wonderfully to lessons about stepping away, sleeping on it, puzzling in spare moments, etc.
One shortcoming is that this exercise is one-and-done: there are no variants, so while it is a wonderful single problem, if a student has seen it before, or wants more after, it’s nonetheless over. Of course, there are alternatives (warning: shameless plug coming!); thinkBio’s own PatternMaster is similar in a broad sense–there is an underlying rule that has to do with relationships among things.
I hope in the future to add to this collection; if you’ve got a favorite, I’d love to hear about it. Note that I make a distinction between rule discovery, as showcased by Petals, and simply figuring out details based on known rules (Battleship, MasterMind, QuantumMine, Sudoku). I believe the former are a deeper representation of the best of ‘real’ science (figuring out how the universe works) than the latter (figuring out details when the rules are already known).