Puzzle: using 4 straight lines, connect all nine dots without breaking the line (i.e. lifting your pen off the paper. Don't do write on your computer monitor, mmkay?). Easy? Can you do it with 3 straight lines?

Display solution: click for the solution - but give it a try first!

A) using only one line

B) using one line of zero length (i.e. using a degenerate line which is a point)

Regarding A) The problem can be solved with a single line if:

- the dots are not infinitely small (as in the 3 line solution)

- you have enough paper to cover the planet (Or at least enough of a strip to go once around the earth)

Just draw a line which goes almost - but not quite - through the three dots at the bottom. The line will go around the planet twice and 'corkscrew' through the remaining points.

If you feel like using less paper just bend a small piece of paper with the puzzle on it into a cylinder.

Reagrding B)

Fold the paper so that all dots touch. Punch a line thrugh the paper. If it is 'ideal' paper (zero thickness) then the line will have zero length. If it is not ideal paper then the folding is a bit more tricky, but you can still do it if you fold it like a crown (a dort at each apex) and have the dots touch.

Abusive comment hidden.(Show it anyway.)Abusive comment hidden.(Show it anyway.)Abusive comment hidden.(Show it anyway.)Abusive comment hidden.(Show it anyway.)Abusive comment hidden.(Show it anyway.)Abusive comment hidden.(Show it anyway.)Abusive comment hidden.(Show it anyway.)but i fell into the trap of thinking of the "dots" as "points"

Abusive comment hidden.(Show it anyway.)Abusive comment hidden.(Show it anyway.)I remember this puzzle from about 50 years ago.

Abusive comment hidden.(Show it anyway.)Abusive comment hidden.(Show it anyway.)Abusive comment hidden.(Show it anyway.)Thanks,

Paul.

PS I will gladly mention your website for more puzzles if appropriate.

Abusive comment hidden.(Show it anyway.)The 4 and 3 line solutions were documented in books. I had not found the other solutions documented elsewhere prior to using them in the presentation. I'm glad to see these other solutions now being written and used.

Abusive comment hidden.(Show it anyway.)Abusive comment hidden.(Show it anyway.)did not.

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