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Connect the dots, A to A, B to B, C to C and D to D. Question
Join the pairs of dots marked similarly (i.e. A to A, B to B, etc.) using four lines which do not cross or touch at any point. The routes must follow the lines of the grid, and may not pass through any of the lettered dots.
A similar, but simpler, puzzle can be found here:
https://proposals.codidact.com/posts/295950
Attribution:
The diagram in this post is a redrawing of the image from the journal that contained this puzzle. I created the diagram using an app on my iPad.
The puzzle design and wording of this puzzle comes from:
EUREKA
The journal of the Archimedeans (Cambridge University Mathematical Society)
No. 33 - October 1970
1 answer
The following users marked this post as Works for me:
| User | Comment | Date |
|---|---|---|
| will.octagon.gibson | (no comment) | Apr 19, 2026 at 20:07 |
Answer
There are likely more solutions than this one just based on which lines get the direct route, and which have to go around.
Strategy
My strategy after failing the naive attempts was to find other ways to go around the destination points near the big circle rather than trying to go around the circle itself, since that's the only way a solution can be reached. The limited vertical space requires going around the individual points instead, at least for a couple of the points.
B and C were the ones I found hardest to connect, so I started with those, but starting with A actually made the solution easier to see. The constriction near the bottom means the lines B-D can only pass through that area once for a solution to be possible, and has to accommodate both C and D near the top of the circle. This is because B needs the space at the bottom. Since C has to go around D, With a direct route for A, it also becomes obvious that B can go around point A with a fairly good margin.
Treating them as pairs of A/B and C/D, one of A/B and C/D can be direct, and the other has to be indirect and go around the other points in its pair. In addition, B has to go around both points C and D. If B takes a more direct route, both C and D would have to squeeze into one line under B, which obviously isn't possible. Any solution where B goes near the top of the circle seems to be impossible in this particular configuration.
Because the map is symmetrical, there's also an (omitted) mirrored solution that can be found by flipping the lines
There's probably a geometric concept that could be used to explain the solution more concisely, but geometry has never been my strong subject :P
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