All Questions
Tagged with combinatorics recreational-mathematics
628
questions
1
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Number of ways to place $4$ kings on an $n \times n$ chessboard
I have an $n \times n$ chessboard and $4$ kings on it. My goal is to count the number of arrangements where some of them are non-attacking or mutually attacking, for example:
In the case where the $4$...
- 159
12
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3
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1k
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Combinatoric Problem in Stardew Valley about Keg Layout
I will first give the mathmatical description of the problem, which I think is a good problem for high school MOers.
Given positive integers $m, n \geq 3$, where $m$ is an odd number, consider a ...
- 507
4
votes
1
answer
161
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Counterexample for a proof
Let $n$ and $k$ be positive integers and
$$T = \{ (x,y,z) \in \mathbb{N}^3 \mid 1 \leq x,y,z \leq n \}$$
be a lattice cube of length $n$.
Suppose that $3n^2 - 3n + 1 + k$ points of $T$ are colored red ...
- 401
-3
votes
1
answer
65
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nth derivative recursive formula
I'm trying to find a recursive series representation of the $n$-th derivative of the following function.
$D^{(1)}_{a, b}(x) = b\sqrt{\frac{p}{q}}D_{a + p - 1, b - 1}(x) - a\sqrt{\frac{q}{p}}D_{a - 1, ...
- 87
1
vote
0
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62
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Number of sets that can be built using length-$n$ combinations of commas and braces
Let $a(n)$ be the number of sets that can be built using length-$n$ combination of either a commas and braces. Here's a manual calculation of $a(n)$ for $0<n<13$ (duplicate sets have been ...
- 1,029
6
votes
0
answers
215
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The sequence $0, 0, 1, 1, 3, 10, 52, 459, 1271, 10094, 63133,...$
Let $a_0$ be a permutation on $\{1, 2, ...,N\}$ (i.e. $a_0 \in S_N$) . For $n \geq 0$:
If $a_n(i+1) \geq a_n(i)$, then $a_{n+1}(i) = a_n(i+1) - a_n(i)$.
Otherwise, $a_{n+1}(i) = a_n(i+1) + a_n(i)$.
$...
- 1,029
5
votes
0
answers
103
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$2$-for-$2$ asymmetric Hex
If the game of Hex is played on an asymmetric board (where the hexes are arranged in a $k\times k+1$ parallelogram), the player who wants to connect the closer pair of sides can force a win, ...
- 3,054
2
votes
0
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119
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Variant of the Hydra Game
I was recently introduced to the Hydra Game by the YouTube channel Numberphile (https://www.youtube.com/watch?v=prURA1i8Qj4).
In this video, they discuss many variants of the Hydra Game - cut off one ...
- 3,337
3
votes
2
answers
97
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Counting $10$ length paths in a $2 \times 4$ rectangle with distance $6$ units from start to end meaning negative moves allowed?
How many different routes of length 10 units (each side is 1 unit) are there to traverse from lower left corner (point A) to top right corner (point B) in a rectangle with 2 rows and 4 column cells ...
- 125
4
votes
1
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146
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Formalising the problem and create a proof for the game "Waffle"
Waffle is an online game at https://wafflegame.net/daily.
It consists in moving letters (swapping them) to recreate the original words. While you have 15 moves, it can be done in 10. I usually try to ...
- 1,125
4
votes
1
answer
119
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Is there a 9×9 Sudoku Room Square?
The following is an order 9 Room square. Copying from Wikipedia,
Each cell of the array is either empty or contains an unordered pair from the set of symbols.
Each symbol occurs exactly once in each ...
- 21.4k
-1
votes
2
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95
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Rectangles Game [closed]
Neznayka draws a rectangle, divides it into 64 smaller rectangles by drawing $7$ straight lines parallel to each of the original rectangle's sides.
After that, Znayka points to $n$ rectangles of the ...
2
votes
0
answers
73
views
Mastermind guessing
I'm reading this problem and I can understand how they got the output for the first four test cases. But the last one I can't really arrive at it. Is there some mathematical concept that I can apply ...
- 67
5
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1
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245
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Taking stones game beginning with 1 to 4 stones in a 2 player game. If we started with 18 stones, is the a winning strategy for the first player?
Amy and Beck are playing 'taking the stones game'. There are 18 stones on the table, and the two people take stones in turns. The first move of the starting player can take 1 to 4 stones. For the ...
- 125
6
votes
2
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257
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2 tables of 6 people: What's a schedule such that all pairs share a table for an equal amount of time?
The problem
There are 2 tables seating 6 people each. With 12 people, how many arrangements (with all 12 people seated) are necessary so that every pair shares a table for the same number of ...
- 1,148