There are 12 dots in a 4x3 grid pattern. You may start at any one point. You must travel as long as you want in a fixed direction, then stop and turn. Again you travel straight till you turn. (Each line segment and angle may be same or different).

What is the minimum lines required?

Hint: It may be an easy puzzle, but requires some out-of-the-box thinking.


1 Answer 1


Assuming we're only thinking as far outside the box as the original 4-lines and 9-dots problem, then unfortunately the answer is 5 lines. There's no way to cover all 12 dots in less than 5 lines even if your lines don't have to start and end on a dot, and the obvious "Z" configuration allows you to do that with all lines starting and ending on a dot.

However, all the other loopholes apply. If you're allowed to go out of the center of the dots, or if the line has nonzero thickness, then you can draw slightly diagonal lines and do it in only 3. If the plane is toroidal or if your line is really thick, then you can abuse the wraparound (or the thickness of the line) and do it in only 1, and so on and so forth.


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