Puzzle 3

Draw three paths, not intersecting and each within the gold region, that join A to A, B to B, and C to C.

Answer

Here's the easy way to answer this puzzle:

1. Consider joining A to A. Observe that there's more than one way to do it, and postpone the decision.


2. Consider joining B to B. Observe that there are two sensible ways to do it, and that they're equivalent by symmetry. Draw one.


3. Consider joining C to C. Observe that there's now only one way to do it. Draw the C–C path.


4. Reconsider joining A to A. Observe that there's now only one way to do it. Draw the A–A path.

No thinking is involved. No backtracking is involved. You just draw in an answer.

The presentation of the puzzle uses a little misdirection, which I assume is deliberate. The order "A,B,C" encourages the solver to try A first. If the letters A and C were swapped, I think most people would find the puzzle easy.

This answers puzzle 3 at A technique in solving puzzles.