Game Goal: Given a pattern of blue and pink gates, find a minimum sequence of ladybug runs that turns all the gates pink. (Click on any 'start' to start the ladybug)
on any of the three 'start' entry points in the first row of tiles, to
start the ladybug down that path.
2. You can reset all the gates to blue by clicking on the 'reset' tile in the far left hand column.
3. You can create your own pattern by first clicking on the 'Create pattern' tile in the far left hand column, and then clicking on any gate to toggle its color. Note that some patterns aren't reachable (i.e. in the orbit of the initial all blue state), and so, for each pattern you create, whether or not it is valid is displayed in the far left hand column.
4. You can speed up or slow down the ladybug by clicking on the 'faster ladybug' ('slower ladybug') tile in the far left hand column.
5. In order to see the effect of running the ladybug through each entry point a selected number of times, without actually running the ladybug, you can click on the 'autorun' tile in the far right hand column. Next, choose how many times you want the ladybug to go through each entry point, and then click on the 'start autorun' tile in the far right hand column.
In addition to being an entertaining diversion, this second variation can be used as a supplement to Richard Singer's paper, Think-A-Dot Group, which is a fascinating exploration of group theoretic concepts emerging from a similar device, leading ultimately to a very well motivated proof of the fundamental theorem of finite abelian groups.
John & kids Fall 2002
Rotating Puzzle Devices
The following applets are Java versions of the rotating puzzle devices in Richard Singer's paper, Secondary Enrichment: Permutation Puzzles.