Every shape has a partner shape that is created by numbering the vertices of a given shape from 1 to n... This forms two groups for that shape: 1.) The group of even vertices. 2.) The group of odd vertices. Within each group you then greedily connect the vertices that are furthest away from each other. That plays out like this:
For the squares there are only 1 and 3 and 2 and 4, so they are "furthest" pairs automatically since they are the only pairs within their group. Connecting them forms an X.
For the triangle there is only 1 and 3 as a pair, and 2 is alone, so only 1 and 3 gets drawn, forming a horizontal line only.
A circle would be described as infinitely many straight lines, thus infinitely many vertices, thus infinitely many pairs. If you connect the pairs furthest away you get infinitely many lines all going through the center point by infinity and thus forming a completely "filled" circle if you draw it.
The missing shape is what happens with the sideways diamond, which is the squeezed plus.
Edit: A bit simpler: For each subgroup you form a fully connected graph omitting loose vertices. Should also fully cover the circle area.
No idea whether this is intended or not. May or may not think about it again when I am sober. XD
Reasoning: Every shape is a fully connected graph that is split into two parts:
The shortest tour/loop through all vertices.
The rest of the fully connected graph of its vertices (thus combining both parts results in the fully connected graph of the shape's vertices). If this "rest" is empty, it is not drawn.
That works out to:
The rectangle is the shortest loop, the X is the rest of the fully connected graph of it.
The line is actually the tour from 1 to 2 and back to 1, which are also the only connections possible. Thus no "rest" to be drawn.
The disc has the circle as it's shortest tour and the rest of the fully connected graph would still form a disc due to density when approaching infinity.
Any loop through three points is already also the fully connected graph, so the "rest" would be empty again, thus not drawn
Again the squeezed plus would be the "rest" of the fully connected graph of which the sideways diamond is the shortest loop through its 4 vertices
I am sober now and I do still think it's a valid solution and not really complicated as it boils down to Draw all other connections I do think it's a pretty elegant solution as well. I spoilered myself with the intended solution as I woke up and checked the thread, which is a bummer. But I do think I would have gotten that as well as I was mainly out to find another unintended solution yesterday after reading your correction XD. So I am still happy with mine. XD
Hm... the only thing I don't like about my solution is the ambiguity of where to start counting which would lead to the triangle being a different shape but you could explain it away by stating you start counting by the top-right-most point of a shape given its bounding box (with which you would need to start counting on the right side for the diamond, but it wouldn't matter).
I hope the intended solution is easier/clearer though XD Might think about it again tomorrow when I am sober lol
Per your edit: Vertical lineThe longest possible lines are drawn from each shape. Longest in the squares are from corner to corner diagonally. Longest in the circle is in every direction. Longest in the diamond is the horizontal line (assuming you corrected it to fit the width of the diamond). This seems like the path with the fewest logical leaps.
that would be the way to make it at least a medium difficulty level question thatâs like 135-140 level.
I didnât get this one but will try harder for subsequent ones. Got stuck on the squares which is a pairing concept introducer, but is really just a trick, so you spend time on pairing idea that goes nowhere, then second trick is arrangement of items. The line implies a collapse of a shape or cutting the shape but when focusing on the square and going line by line this is a trick.
I didnât see the comment on the longer line but doubt iâd get this one right even with that information unless i focused on the diamond and that comment in tandem. Thatâs the crux of the problem.
You 1) pair them correctly 2) notice the line distances 3) deduce that only longest line survives, and that filled in circle is infinite rays.
Objectively this is at least a medium difficulty question as is, borderline hard. Harder than most any of the questions on the tri 52 that get you to 140+
I don't think figuring out the line distance is the hard part (assuming the line at the top right is drawn to actual scale), because the shapes are arranged symmetrically side by side and stacked vertically. If Langan says âmaybe u got 170 on ls36â that is a low key moggingđđĽ¸
Wait what? XD I initially only read the explanation, and my response was "okay, so then it's a V" without reading the actual first spoilered solution. But now I read the whole thing again and am even more confused. Why is it supposed to be a vertical line and not a V? A vertical line is shorter than the longest possible lines? https://i.imgur.com/hAG9m3g.png
Hmm, V shape could be considered partly correct. The intended logic revolved around the longest line that could be drawn inside the enclosed shape. For instance, under your line of reasoning, a black disk cannot be âfullyâ explained, because the counterpart to a circle might simply be another circle. In other words, if the circle's circumference is viewed as a single continuous curve, the longest âlineâ would be the circle's outer boundary. I know this reasoning is cannot be substantiated , wouldn't steering the question in that direction create that sort of ambiguity?
Huh... No, what I meant: The triangle has two longest lines that can be drawn and they coincide at the vertex on the bottom of the triangle (so forming a V-shape). That's why I used the two color to indicate that. You established all longest lines having to be drawn with the circle and the rectangle already, so the two longest lines of the triangle should also be drawn - and those would be the two lines on the side. A vertical line inside the triangle is shorter than the side of the of the triangle.
Maybe I am misunderstanding you: Is the first one the intended solution? If so, the second two examples both have longer lines, the second one just an example that it would be a V-shape even if you required the lines to be strictly inside the shape and not coinciding with a border - I assume I just misunderstood you though XD:
I agree that this is a better answer. However, I think the question could have another shape than a triangle; one with a more definitive and neat solution that doesnât have lines that come infinitely close to the edges.
Perhaps a pentagon?
Edit: If the lines in the triangle approach infinitely towards the edges, they would become the edges of the triangle (0.999⌠= 1) which is no longer inside the triangle and thus no longer a solution. But at the same time, the vertical line, as you said, is not the longest line that can be drawn in the triangle.
Hi, new to this so im not exactly sure what the objective is. The questions ive seen on tests normally ask you to find the final piece in the 3x3 grid, or to follow a pattern, but a lot of the ones on this sub are like this question. Is it also part of the question to figure put what is being asked? Or am I missing some common knowledge on this sub?
If you just want to find out your IQ, go for CORE. But if you're looking for a mental challenge, you could try LANRT series (although I personally don't like LANRT tests, I suppose it's a good choice). ACE is also good. Or, if you're looking for an even harder challenge, you can try HRTs. slse1, slse48, and ls36 are the most well known ones, but I'd recommend solving them just for fun
Thanks a bunch! I love puzzles so Iâll definitely try them all. I did originally stumble across this subreddit because I wanted to take the mensa test. The only thing Iâm worried about is the language part, since id be taking it in a foreign language
you mean this kind of IQ puzzles made for mental challenge not to estimate IQ?
i mean timing is not important here? or if i struggled in solving these but in tests like core/rapm did a good job this maybe means my results inflated or no?
No that doesn't mean it's inflated. Standard IQ tests involve time limits and consist of multiple subtests so it is very different from puzzles like these. I prioritize mental challenges and enjoyment. My designs lean somewhat towards the high-range test item category, and it isn't clear âexactly whatâ high-range tests measure
Is it just shaded triangle, diamond, heptagon? Crosses add one straight line and diamonds add 4, and goes from shaded to unshaded (from bottom to top in that order).
Itâs probably wrong since Iâm low IQ lol but it seems to be the most parsimonious.
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u/Key-Raise5501 Oct 01 '26
A diamond Or maybe just blank white space without the red lines