# Number Puzzle #6 – Solution

Two days ago, I posted this simple little number puzzle. Quite a few folks came up with the answer below.  One of the interesting questions you can ask is whether that solution is unique.

Clearly there are two lines of symmetry in the original problem so by reflection alone we come up with a total of four solutions: $\{ I, F_x, F_y, F_x \circ F_y \}$ where $F_x$ and $F_y$ represent “flips” across the lines of symmetry and $I$ represents the identity, or the solution above.  By $F_x \circ F_y$, I mean the composition of the flipping operations or just consecutive flipping.

There also exists radial symmetry at $180^{\circ}$, but this is equivalent to $F_x \circ F_y$.  So for this arrangement above, there are four solutions of the same “type”.

Are any other arrangements possible besides these four?