| Math Mojo - Making Math Meaningful |
Connecting
9 circles with only 3 straight, continuous lines
(in this
puzzle, the word "line" is meant to mean "line segment".)
Here is the puzzle. Remember to try it on paper before you try it here.
The reason this can work like that, is because of the wording.
In the introduction to the puzzle (on the Puzzle Page) I mentioned that most people don't differentiate between "circle" and "point."
Had the puzzle been stated, "Connect 9 points arranged in a square, with 3 continuous, straight lines," we couldn't use this solution.
A point has no dimensions. This solution works because a circle has two dimensions, and we used one of them to sort of "cheat" to get the lines through them.
A line can only pass through one point in a point, because a point only has one point. On the other hand, a circle has lots of them.
The main Idea about this, is that a circle is not a point. It only represents a point. It is a "picture" of a point, so to speak. But a picture is not the thing it represents, it is just a picture.
In other words: The map is not the territory. This is a good lesson to learn for solving problems.
People who think "out of the box" might be able to solve the puzzle with 4 lines. But some people only think "out of the box" in order to get into another box. They don't realize there are vastly different ways to think.They are the ones who wouldn't get the solution for 3 lines, and also wouldn't understand why it wouldn't work with points.
return to circles and lines puzzle page
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