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A puzzle related to shapes, geometric objects (polygons, circles, solids, etc.) of any number of dimensions, the relative position of figures, and the properties of space. Use with [mathematics]

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Score of 3
2 answers
271 views

This is not an original, I saw it today (link given in spoilers - also shows solution, so really is a spoiler...) Squares, triangle and circle puzzle This puzzle was shown to me today. I think it is ...
Score of 15
1 answer
399 views

This is part of the Monthly Topic Challenge: Obscure Observances The coloured map puzzle I work at a small delivery company (not a true story) that has five warehouses. Recently, I commissioned an ...
Score of 6
1 answer
225 views

Can you construct a bijection $f:A\to B$, where $A,B \subset \mathbb R$ are closed intervals, such that the graph of $f$ is invariant under rotations by $\pi/3$ about the origin? Bonus: Can you do ...
Score of 1
1 answer
225 views

EDIT: I realized my wording was ambiguous and even misleading, because it allowed for two opposite interpretations. I hope now that the construction is clear. Introduction: The topological gods were ...
Score of 15
2 answers
978 views

You are an ant walking on the gridlines of a torus. For this puzzle, we are going to use these representational conventions: All toroidal surfaces are represented as an $n\times m$ grid, where $n,m \...
Score of 8
2 answers
296 views

I have three hand-fans, each made of a 120°-sector of unit radius (the fan) attached to a line segment of unit length (the handle). I arranged them symmetrically as shown in the figure below so that ...
Score of 11
1 answer
382 views

The animation shows a triangular pendulum in a regular pentagon. The red angles are equal. What is the maximum ratio of the blue to yellow areas?
Score of 11
4 answers
716 views

Four congruent yellow stars (regular pentagrams) are arranged as shown below, touching only at the corners. A black rhombus aligned with some of the stars’ sides is drawn. Can another star, congruent ...
Score of 7
1 answer
259 views

You have an equilateral triangle and an inscribed circle. On each of the three sides, a point is randomly chosen (all points equally likely to happen). You connect each of the points to the opposite ...
Score of 8
1 answer
242 views

It is known from research on small cases of the no-three-in-line problem that 2n points can be placed on an n × n grid in such a way that no three points are collinear for at least n ≤ 64. A slightly ...
Score of 5
1 answer
237 views

Fold the shape (the white region) into a rectangle such that the rectangle is 360 layers thick everywhere. A puzzle for this type of orgami puzzle game made by Ωmega_3301, similar to this question.
Score of 6
1 answer
242 views

What proportion of the outline pentagram is covered by the inner pentagrams? The illustration only shows 4 levels of iteration of pentagram, but consider if the series went to the tip of the outline ...
Score of 8
2 answers
386 views

A use of the Monthly Topic Challenge grid. The following 15 by 15 grid has 160 white cells: Using the same 15×15 grid with 160 white cells: A tiling using only one pentomino type is impossible. (ref) ...
Score of 8
2 answers
358 views

A use of the Monthly Topic Challenge grid. The following 15 by 15 grid has 160 white cells: It is not tileable by copies of any single pentomino. (ref) However, if we allow mixed pentominoes, the ...
Score of 6
1 answer
343 views

You are given a square piece of paper and your task is to fold it into a regular pentagon. No additional tools are required (apart from a flat table to make proper folds). Note the lateral thinking ...

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