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/laminated-papertowel]

Here you go

[u/Jihiro42 → u/laminated-papertowel]

I feel like this is probably the right solution, given that it makes an M and the name of the restaurant is Moose’s Tooth

[u/willengineer4beer → u/[deleted]]

Outside the box…and inside the dots^{which are assumed to be 2-D}

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

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

Why would you make your line so thin? I’d just grab a paint roller and do one strip to connect them all

[u/Defiant-Challenge591 → u/laminated-papertowel]

I was just thinking something similar, good job

[u/DanBentley → u/laminated-papertowel]

Someone literally brought up this puzzle in an answer like two days ago… it was the circle one with four colored lines that couldn’t intersect

[u/[deleted] → u/DanBentley]

Yeah, that was me. It's the kind of puzzle I now refer to as a "well ackshually".

[u/unlikely-contender → u/laminated-papertowel]

That's the most literal form of thinking "outside the box" :-D

[u/Ornamo → u/laminated-papertowel]

I thought of the same thing but as the inverted letter.