I invented a puzzle, inspired by Simon Tatham's Portable Puzzle Collection. Is there anything that it could improve on? Was it too easy, or was it too hard? Anything I could add? What must I call it?
Is this the right site to post this? Perhaps Meta is better.
Puzzle:
You have the following grid: $$\begin{array}{|r|c|} \hline \rm A &\rm B &\rm C \\ \hline \rm D &\rm E &\rm F\\ \hline \rm G &\rm H &\rm I\\ \hline \end{array}$$ The letters represent numbers ranging from $1$ to $4$ inclusive. They cannot all be the same number, but all the numbers from $1$ to $4$ don't have to be in the grid either... but there's a catch.
You have to draw a path from the left bottom corner of the grid to the top right corner, following the edges of the squares. That includes outer edges as well. The path cannot cross an edge more than once, but it can meet an intersection more than once (intersections are corners/vertices with four edges that join to it). The numbers in each square in the grid show how many edges of that square must be crossed with the path. Here is an example:
Example:
Find the path. $$\begin{array}{|r|c|} \hline \rm 1 &\rm 3 &\rm 2 \\ \hline \rm 1 &\rm 2 &\rm 3\\ \hline \rm 2 &\rm 1 &\rm 1\\ \hline \end{array}$$ SOLUTION:
There might be more than one solution, but I hope this puzzle is fun. Try it with the following one. Remember, you can't cross an edge more than once, but you can meet an intersection more than once.
Challenge:
Find the path. $$\begin{array}{|r|c|} \hline \rm 4 &\rm 3 &\rm 3 \\ \hline \rm 3 &\rm 4 &\rm 4\\ \hline \rm 3 &\rm 4 &\rm 2\\ \hline \end{array}$$
Edit:
Made a harder one.
Find the path. $$\begin{array}{|r|c|} \hline \rm 2 &\rm 3 &\rm 3 &\rm 3 &\rm 2\\ \hline \rm 2 &\rm 4 &\rm 3 &\rm 2 &\rm 3\\ \hline \rm 2 &\rm 1 &\rm 2 &\rm 3 &\rm 2\\ \hline \rm 3 &\rm 3 &\rm 3 &\rm 3 &\rm 1 \\ \hline \rm 3 &\rm 3 &\rm 1 &\rm 2 &\rm 3 \\ \hline\end{array}$$
Okay, apparently this was impossible, as declared by comments below, with a formal proof given by @JonMarkPerry. I must admit, my ones do look like twos (with the only thing differing them being their curvature, so my messy handwriting does not do to well). I believe in the first column, all the ones are supposed to be twos. I have fixed that now, and have tried it three times.