All Questions
Tagged with combinatorics recreational-mathematics
627
questions
4
votes
1
answer
161
views
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
60
views
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, ...
- 79
-1
votes
0
answers
43
views
What is the number of all weak compositions of $10$ into $5$ parts so that exactly two parts are $0$?
What is the number of all weak compositions of $10$ into $5$ parts so that exactly two parts are $0$ ?
Firstly could someone explain the difference between a weak composition and a composition.
Also ...
- 3
1
vote
0
answers
62
views
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
views
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
views
$2$-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
answers
115
views
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 ...
- 3,225
3
votes
2
answers
97
views
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
answer
141
views
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
views
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
answers
94
views
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
votes
1
answer
240
views
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
answers
255
views
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
2
votes
1
answer
124
views
Prove that no closed knight's tour is possible on the $2 \times 2 \times 2 \times 2 \times 2 \times 2$ chessboard
Let $n,k \in \mathbb{N}-\{0,1\}$. The generalization of the closed knight's tour problem to higher dimensions asks to move a knight along the $n^k$ cells of a $n \times n \times \cdots \times n$ ...
- 1,160