All Questions
8
questions
0
votes
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74
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find all positive integers n for which there exists a certain $n\times n$ table where each entry is I,M, or O
Find all positive integers $n$ for which we can fill in the entries of an $n\times n$ table with the following properties:
Each entry can be one of $I,M,O$;
In each row and each column, the letters $...
- 1,137
0
votes
1
answer
126
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Resizing a matrix
I have a problem of resizing a rectangular matrix into a square matrix with certain restrictions:
Suppose you have a rectangle of size $m\times n$, and wlog $m> n$. Now i want to resize this ...
- 2,632
4
votes
0
answers
206
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Derive formula for number of tilings of an $m \times n$ board.
I have tried to find the derivation of the formula for the number of tilings of an $m \times n$ board with $2 \times 1$ tiles which is the following.
$$\prod_{k=1}^{m}\prod_{l=1}^{n} \left(4\cos^2{\...
- 275
0
votes
1
answer
72
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How to count tilings on a $2 \times n$ board using the adjacency matrix?
I am trying to find the number of distinct possible tilings of $2 \times n$ board using only $2 \times 1$ tiles, such that no tiles overlap, go beyond the board boundary and the board is completely ...
- 275
7
votes
0
answers
266
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Sequential square packings
There are various studies for packing sequential squares of size $1$ to $n$. We can try to find the smallest square they will pack into, as in tightly packed squares. We can find the smallest square ...
- 21.4k
7
votes
2
answers
794
views
Same Diagonal Dissection
Divide a rectangle into smaller rectangles with two criteria:
All sub-rectangles must have different sizes.
All sub-rectangles must have diagonals with length 1.
What is the smallest possible ...
- 21.4k
0
votes
1
answer
399
views
number of ways to fill a 2D grid
We have a 2D grid with n rows and m columns, we can fill it with numbers between 1 and k (both inclusive). Only condition is that for each r such that 1<=r<=k ,no two rows must have exactly the ...
- 315
6
votes
1
answer
270
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Constructing Magic Squares over $\mathbb{Z}$ from Magic Squares over $\mathbb{Z}_m$
A magic square over $\mathbb{Z}$ is an n x n matrix whose entries are $\{1, \ldots, n^2\}$, with the sum of every row and column identical (in particular, my magic squares are all normal, but the sum ...
- 7,051