All Questions
Tagged with combinatorics recreational-mathematics
628
questions
2
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3
answers
500
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Squares on a checkerboard
How many squares of all sizes arise using an $n$-by-$n$ checkerboard?
How many triangles of all sizes arise using a triangular grid with sides of length $n$ ?
- 497
1
vote
1
answer
143
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Need help on proceding a paper about estimating numbers of sudoku
I was reading a paper that I found via spiked math (http://spikedmath.com/comics/424-the-numbers-quiz-solutions.png): http://www.afjarvis.staff.shef.ac.uk/sudoku/sudoku.pdf.
I have problem ...
- 819
4
votes
2
answers
1k
views
Minimal number of solutions to a sudoku cube
A "Sudoku cube" is a 3x3x3 uncoloured Rubik's cube. In the solved state, each face has the digits 1 through 9 arranged in ascending rows from top to bottom, and all of the digits on a given face have ...
- 527
14
votes
3
answers
1k
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Tiling a 7 x 7 square with 15 "I"-trominoes and 1 "L"-tromino and one unit square
My teacher gave us a riddle that goes like this:
You have a $7\times 7$ square and $16$ $3\times 1$ tiles.
Of the $16$ tiles, $15$ are straight and $1$ is crocked ("L" shaped).
When you tile the ...
- 143
79
votes
9
answers
85k
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What is the math behind the game Spot It?
I just purchased the game Spot It. As per this site, the structure of the game is as follows:
Game has 55 round playing cards. Each card has eight randomly placed symbols. There are a total of 50 ...
- 894
11
votes
1
answer
1k
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Solving a scrambled $3 \times 3 \times 3$ Rubik's Cube with at most 20 moves!
I read somewhere that any scrambled form of $3 \times 3 \times 3$ Rubik's cube can be solved using at most $20$ moves, and I just said "wow"! I am wondering can we prove this by mathematical ways? Or ...
- 4,896
14
votes
2
answers
1k
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any pattern here ? (revised 2)
for any positive number $k$, I have a $(k+1)*(k+1)$ matrix. I wonder if these matrices follow any "obvious" pattern. My goal is to guess the elements for matrix with $k=5$ and above (most probably in ...
5
votes
2
answers
459
views
Natural set to express any natural number as sum of two in the set
Any natural number can be expressed as the sum of three triangular numbers, or as four square numbers. The natural analog for expressing numbers as the sum of two others would apparently be the sum ...
- 2,301
16
votes
2
answers
2k
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Rubik's cube interesting questions?
The upper bound for the number of moves required to solve a regular Rubik's cube has been shown to be 20.
Two questions come to mind:
Does this result have more general significance?
What are the ...
- 2,280
13
votes
3
answers
6k
views
Lights out game on hexagonal grid
I greatly enjoyed the Lights Out game described here (I am sorry I had to link to an older page because some wikidiot keeps deleting most of the page).
Its mathematical analysis is here (it's just ...
- 2,280
5
votes
2
answers
916
views
How many ways can I make six moves on a Rubik's cube?
I am writing a program to solve a Rubik's cube, and would like to know the answer to this question.
There are 12 ways to make one move on a Rubik's cube. How many ways are there to make a sequence of ...
- 163
4
votes
2
answers
421
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How is done the calculation of the minimum number of movement to solve any configuration of Rubik's Cube?
I have read a few weeks ago that some mathematical researchers have discover that the minimum number of movements to solve any initial configuration of a Rubik's cube has been downsized to 20.
How do ...
- 143
14
votes
2
answers
929
views
How many disconnected graphs of the Rubik's cube exist?
Let us say that a Rubik's cube in a particular configuration is in a particular "state". All other configurations of this cube (other "states"), which can be achieved by rotations of the cube can be ...
- 241