# Invariance Principle (*Note: This is a relatively imprecise concept so there is not a universally accepted terminology for it, but for the problems dealt with on this site we need a name for it.*) The **invariance principle** is a technique useful for figuring out the answer to a puzzle under the assumption that such an answer exists and is unique. It applies when a puzzle is not be completely determined by the constraints (which might be in the form of a diagram) and yet there is a unique answer. This means that there are multiple possible diagrams that can be drawn. This invariance can be exploited in two ways, either to get an actual solution or as a route to solving the general case. This is sometimes referred to as the _Agg Invariance Principle_ due to the frequency with which it can be used to solve [[Catriona Agg]]'s [[geometry problems]]. ## Strong Invariance The **strong invariance principle** applies when there is a way to draw the diagram which makes it straightforward (or, at least, more straightforward) to see the solution. Often this involves exploiting a particular symmetry or coincidence of this special case. ## Weak Invariance If there isn't a way to draw the diagram to make solution obvious, it still might be possible to use the variety of possible diagrams to reveal a route to a solution. This is the **weak invariance principle**. A common application is to mark on the diagram the possible locations of certain of the points in the diagram, these might be on a line or a circle. A good strategy for finding a solution to the general problem is then to prove directly that the shape is what it appears to be. [[!redirects invariance principle]] [[!redirects invariance principles]] [[!redirects Agg invariance principle]] [[!redirects weak invariance principle]] [[!redirects strong invariance principle]]