Eleanor's cousin introduced her to the "dot" game: you take a grid with dots, each person draws a line connecting two adjacent dots (north, south, east or west), and if you draw the fourth line creating the square you write your initial in it and go again. Here's the wikipedia article, if you're interested.
Eleanor drew her own (slightly wobbly) grid with 100 squares. She was quite impressed with the grid and she was convinced that her mother would much rather play dots with her than clean the kitchen. I actually felt as though I had paid my dues playing the dots and boxes game when I was younger, but I started playing just to spend time with her. I was expecting to be bored, try to help her win, and go back to cleaning.
Almost immediately Eleanor decided we should change the rules for the game. Now you didn't have to connect adjacent dots, you could connect any dots, as long as you didn't go through another dot or cross another line. When you completed a polygon of any shape, you wrote your initial in it, although this polygon could be further subdivided (Eleanor loved this technique). This made the game much more fun and unfamiliar. It did increase in theory the number of lines that could be drawn, but the limitations decreased the number of lines that were actually drawn. The grid after playing was much more attractive and interesting.
The best part is that it wasn't boring at all: there are plenty of mathematical and strategic questions I would like to answer. I wonder if this is a good game, or if there are strategies I haven't thought of which make it trivial. We kept score by the number of boxes, but it might be more interesting to keep score by total area covered (probably you'd need a computer to do the figuring). Also, the rule about subdividing already completed polygons might have to be revisited. If you keep score by area, the game seems like it might be related to Go.
Anyway, I was impressed by Eleanor's creativity. Also by her ability to keep her mother fascinated by a game I thought I had already played out.
Eleanor drew her own (slightly wobbly) grid with 100 squares. She was quite impressed with the grid and she was convinced that her mother would much rather play dots with her than clean the kitchen. I actually felt as though I had paid my dues playing the dots and boxes game when I was younger, but I started playing just to spend time with her. I was expecting to be bored, try to help her win, and go back to cleaning.
Almost immediately Eleanor decided we should change the rules for the game. Now you didn't have to connect adjacent dots, you could connect any dots, as long as you didn't go through another dot or cross another line. When you completed a polygon of any shape, you wrote your initial in it, although this polygon could be further subdivided (Eleanor loved this technique). This made the game much more fun and unfamiliar. It did increase in theory the number of lines that could be drawn, but the limitations decreased the number of lines that were actually drawn. The grid after playing was much more attractive and interesting.
The best part is that it wasn't boring at all: there are plenty of mathematical and strategic questions I would like to answer. I wonder if this is a good game, or if there are strategies I haven't thought of which make it trivial. We kept score by the number of boxes, but it might be more interesting to keep score by total area covered (probably you'd need a computer to do the figuring). Also, the rule about subdividing already completed polygons might have to be revisited. If you keep score by area, the game seems like it might be related to Go.
Anyway, I was impressed by Eleanor's creativity. Also by her ability to keep her mother fascinated by a game I thought I had already played out.
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