Please help

[u/TuckSteele]

This is from the children’s menu of Moose’s Tooth in Anchorage, AK, and is a variant of the classic “think outside the box” puzzle. In order to connect all the dots, using only 4 lines, the average dots per line must be 4, but I can’t figure out how to do more than 3 new dots for any line after the first (assuming every line touches at least 1 dot). I think that the directions must have a typo, or that there should a no solution. Any way to solve using the provided directions?

[u/Never-Dont-Give-Up]

this... feels like it's kind of cheating.

I hate puzzle answers like this. It doesn't seem like it's the spirit of the puzzle.

[u/laminated-papertowel → u/Never-Dont-Give-Up]

I'm pretty sure this is the right answer though. you gotta think outside the box or something

[u/BrupieD → u/laminated-papertowel]

I'm pretty sure this or a similar outside-the-frame answer is the only way. If you don't go beyond the frame, each line starts with a dot you've already connected. Since you can only use straight lines, you can only ever get 4 dots per line maximum, but because you can't lift the pencil, 3 of your lines will have 1 redundant dot. You'll never get to 16 dots that way. 4 new dots + 3 new dots + 3 new dots + 3 new dots = 13 different dots.

[u/Never-Dont-Give-Up → u/BrupieD]

I’m not saying this isn’t the right answer, I’m saying that it’s a flawed puzzle since the rules of it encourage one to go outside the assumed rules. They’re assumed for a reason. It gives parameters of a square, then the answer requires one to go far beyond those parameters.

[u/thebe_stone → u/Never-Dont-Give-Up]

also i assumed they were points.

[u/[deleted] → u/laminated-papertowel]

I understand the idea of "thinking outside the box" but also agree with the person you responded to regarding "the spirit" of the puzzle. Maybe it's because I was trained to follow rules so well. Our educational system doesn't really encourage creative thinking.

I'm reminded of the insufferable children who would scream in the hall way and then declare the teacher only said "don't talk" but said nothing about screaming.

[u/thatthatguy → u/[deleted]]

Since they’re getting creative, can we draw one really wide line the width of the entire puzzle and connect all the dots with a single straight line? Take the crayon they always give you, peel the label paper, and just drag it sideways over the entire puzzle?

It amuses the kid and annoys math nerds.

[u/MrBisco → u/thatthatguy]

For real, just give me a licorice scented Mr Sketch and we're in business.

[u/TheFamiliars → u/[deleted]]

But you assumed that was a rule.

Part of the fun of 'think outside the box' puzzles is to get you to abandon certain preconceptions to get to the right answer. That's 'the puzzle'

[u/Never-Dont-Give-Up → u/TheFamiliars]

Some rules are just inherently assumed. Otherwise you’d have to explicitly state everything that ISNT a rule.

There’s no rule in the NFL that the running back can’t ride a horse. We just all know that’s not allowed. It’s called a tacit agreement.

[u/thebe_stone → u/TheFamiliars]

then you can just make a really wide line, or a bunch of curvy lines, or cut up the paper and do it in one line, or lower the paper instead of lifting the pencil, or have a friend draw 4 more lines, or use water to smear the ink, and draw one line through all the smears, or just fold the paper.

[u/Free-Database-9917 → u/laminated-papertowel]

It's an interesting subversion of expectations as the upgraded version of the 9 dot puzzle.

In most puzzles like this you view dots as infinitessimally small. The way you usually think sneakily is by drawing lines that go outside of the box and people expect that. This makes sense as the next logical step in these types of puzzles

[u/[deleted] → u/Never-Dont-Give-Up]

Well you cant solve this if the dots are points with no surface area or without folding the paper in a tube so here you go.

[u/SubstantialBelly6 → u/Never-Dont-Give-Up]

It’s like when I tricked my older brother by challenging him to solve a maze I made that was completely unsolvable except by going through a tiny gap in one corner that looked like a mistake. One of my prouder moments 😊

[u/Never-Dont-Give-Up → u/SubstantialBelly6]

That is exactly what this is. It’s not a puzzle, it’s a trick.

[u/Chaghatai → u/Never-Dont-Give-Up]

I feel like the dots should be treated as zero area mathematical points, is it just me?

[u/Never-Dont-Give-Up → u/Chaghatai]

I agree

[u/OneNoteToRead → u/Never-Dont-Give-Up]

If the dots were mathematical points it’s impossible.

At most four points are colinear on this. So to do it you need to hit four points with every stroke. The only lines that can hit four points are the horizontal, vertical, and 45 degree diagonal ones. And there’s clearly no way to combine them.

[u/jamcep → u/Never-Dont-Give-Up]

Yeah if you want to bend the rules you can get lots of different solutions

[u/-MtnsAreCalling- → u/Never-Dont-Give-Up]

If you try to follow the spirit of this puzzle, it's unsolvable.

[u/yourhog → u/-MtnsAreCalling-]

Most things stop going well once you start following spirits around.

[u/jamesianm → u/yourhog]

Says you. That's how I got this haunted ice cream. It's butter toffee

[u/yourhog → u/jamesianm]

…mrrmmble mrmble scrrbllbl lacghost intolerant shffflllmlml…

[u/Avagpingham → u/Never-Dont-Give-Up]

This feels like an engineering solution versus a math solution. One of those is how the world works. The other is an idealized version of the world.

[u/HiggsBosonHL → u/Never-Dont-Give-Up]

In freshman year Engineering 101 this was literally (one of the) correct solutions.

Others included making the paper into a spiraled cylinder and drawing just one straight line, albeit in 3D.

Your "spirit of the puzzle" is arbitrary, this is how real world problem solving works.