All Questions
33
questions
2
votes
0
answers
75
views
Smallest number of groups
Eighty-four developers sign up to contribute to a public open-source project. You need to divide the developers into $n$ subteams such that each contributor is on exactly one team. Their personalities ...
- 378
3
votes
1
answer
187
views
How to prove whether this grid puzzle is unsolvable/solvable?
[Disclaimer: I have researched a bit before this post and I have found no other questions that address my problem specifically, hence this post]
So I have been made a puzzle concept in a python ...
- 33
2
votes
2
answers
198
views
Shapes made of concave and canvex curves combination problem
I have been working on this particular problem for a considerable amount of time. The problem is as follows:
[[ Image of problem ]]
In the $7$-by-$7$ grid above, one can draw a simple closed curve ...
- 23
4
votes
1
answer
121
views
How to determine if this graph is planar?
I was doing a graph theory text book where one of the problems asks:
Is this graph planar?
As this graph contains a triangle, the best bound for $e$ is $3v-6$ which this satisfies $(14<18)$
So then ...
- 1,863
7
votes
1
answer
262
views
Given n squares, in how many ways can they be contiguously arranged into a single shape?
Context:
At school today, a friend of mine ripped up a piece of paper he had written on. I was considering the number of possible ways I could rearrange these individual pieces to try to reconstruct ...
- 172
0
votes
1
answer
62
views
A combinatorial problem of counting path weights with a special symbolic binary tree
Consider two symbols, $X$ and $Y$.
Symbol $X$ spawns $X$ and $Y$ -- think of the spawning as a binary tree rooted in $X$ with two leaves. The path weight for leaf $X$ is $a$ and that for leaf $Y$ is $...
- 545
6
votes
2
answers
851
views
Towers of Hanoi if big disks can go on top of small disks
The Tower of Hanoi puzzle is concerned with moving $n$ disks between three pegs so that a larger disk cannot be placed on top of a smaller disk. Based on a (now deleted) StackOverflow question, ...
1
vote
2
answers
145
views
Couple problems and classic wolf/goat/cabbage and abstraction
I was reviewing Dijkstra's approach on the problem/puzzle of how 2 married couple can cross a river with 1 boat that can carry 2 people. The original problem's restriction is that the wife can't be in ...
- 1,609
1
vote
1
answer
269
views
number of closed-loop graphs in square lattice
Suppose I have a $N\times N$ square lattice. I want to know how many different closed-loop diagrams are there. The closed-loop diagrams can have no loop, one loop, two loops, etc. If two loops share ...
- 185
0
votes
1
answer
274
views
Non-attacking knights and rooks on a chessboard
This question from math contest olympiad phystech I tried to find the solution but I can't find it. Please help me to find solution of this problem.
Given a board with a size of $11 × 11$ cells. Jack ...
- 161
3
votes
2
answers
337
views
minimal average distances between $n$ nodes in a directed graph
I have a directed graph with $n$ nodes.
for any paired of nodes $A,B$, there is a directed edge that goes in between, but it can't go both ways. i.e. $A \rightarrow B$ and $B \rightarrow A$ cannot ...
- 789
2
votes
2
answers
124
views
Removing nodes from graphs such that one is dependent on other - ZIO $2010$, P$1$
Greetings Community! The above problem you see is a combinatorics problem I could not solve. :( This problem is from ZIO $2010$, P$1$.
Here is what I did: Observe that every graph can be divided ...
- 779
2
votes
1
answer
1k
views
How to calculate minimum number of games in round robin with more than two players per games
Suppose you have n players in a tournament. In each game, exactly 4 players play against each other. What is the minimum number of games needed such that every player has played every other player at ...
- 596
10
votes
1
answer
857
views
Minimum number of dominoes on an $n \times n$ chessboard to prevent placement of another domino.
OEIS sequence A280984 (based on this Math Stack Exchange question) describes the
minimum number of dominoes on an $n \times n$ chessboard to prevent placement of another domino.
The sequence ...
- 5,072
8
votes
1
answer
182
views
Uniqueness of spanning tree on a grid.
When I was at the Graduate Student Combinatorics Conference earlier this month, someone introduced me to a puzzle game called Noodles!.
The game starts with a collection of "pipes" on a grid ...
- 5,072