All Questions
10
questions
0
votes
2
answers
144
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A beetle on each square of a $9 \times 9$ chessboard. Each beetle crawls one square diagonally, find minimal possible no. of free squares.
Question:
A beetle sits on each square of a $9 \times 9$ board. At a signal each beetle
crawls diagonally onto a neighboring square. Then it may happen that
several beetles will sit on the same ...
- 5,316
3
votes
3
answers
121
views
Coloring the faces of n^3 unit cubes s.t., for each color j between 1 and n, the cubes can be arranged to form nxnxn cube with j-colored outer faces
I encountered the following problem in Paul Zeitz's The Art and Craft of Problem Solving (problem 2.4.16 on page 56 of third edition):
Is it possible to color the faces of 27 identical $1 \times 1 \...
- 155
0
votes
0
answers
87
views
3 points blue, red, green form a triangle $T$ in $\mathbb R^2$. 3 points B, R, G inside that triangle. Do all proper rainbow triangles cover $T$?
Suppose I have 3 points colored blue, red, and green resp. forming a triangle $T$ in $\mathbb R^2$. Suppose I have 3 more points colored blue, red, green resp. (possibly overlapping) in the interior ...
- 8,945
4
votes
0
answers
4k
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Intriguing moves with the $3\times3\times3$ Rubiks cube
Preface
This is a recreational problem I kinda figured out during my free time playing around with the Rubik cube, so I hope everyone will take it as chilling as I did.
Okay, so for those of you who ...
- 1,288
-1
votes
2
answers
94
views
Question regarding numbers on chessboard
On one square of a 5×5 chessboard, we write -1 and on the other 24 squares +1. In one move, you may reverse the signs of one a×a subsquare with a>1. My goal is to reach +1 on each square. On which ...
- 338
8
votes
2
answers
203
views
Is it possible to cover an $11 \times 12$ rectangle with $19$ rectangles of $1 \times 6$ or $1 \times 7$?
Is it possible to cover an $11 \times 12$ rectangle with $19$ rectangles of $1 \times 6$ or $1 \times 7$?
Attempt:
There should be $132$ unit squares to be covered. Since there are $19$ rectangles ...
- 4,855
4
votes
2
answers
599
views
Circle-separable colorings of finite set of points in the plane
This is problem 12093 of the American Math Monthly, published a few months back:
Let $S$ be a finite set of points in the plane no three of which are collinear and no four of which are concyclic. A ...
- 1,914
6
votes
1
answer
653
views
How many colors are needed to color an infinite grid so that no sqaure have the same color in all 4 vertexes? [duplicate]
Suppose on a 2 dimension infinite grid, all nodes, or equivalently, all $(p,q)$ points, where $p, q \in \mathbb Z$, need to be painted with a color.
Is there a way that, given enough kinds of paiting ...
- 5,355
2
votes
1
answer
206
views
A problem of colours of vertices in equilateral triangle
I have a problem with this exercise. I spent a lot of time, but I didn't figure out anything at the moment. Maybe anyone could help me?
An equilateral triangle, with side lenght $n$, is divided into ...
- 914
4
votes
0
answers
172
views
Maximal unit lengths in 3D with $n$ points.
Given $n$ points in 3D space (V), what is the maximal number of unit distance lengths (E) between those points? Here are a few possibilities. Some of them are chromatic spindles.
A collection of ...
- 21.4k