All Questions
Tagged with optimization graph-theory
30
questions
8
votes
3
answers
1k
views
Largest sequence of adjacent numbers less than 11 such that adjacent number divides the other
Friday writes different positive whole numbers that are all less than 11 next to each other in the sand. Robinson Crusoe looks at the sequence and notices with amusement that adjacent numbers are ...
- 3,193
6
votes
2
answers
349
views
While 2024 arrives
There are about $9.266 \times 10^{45}$ partitions of 2024, a handful! To each of these partitions corresponds a graph in which the vertices are each of the parts, two of which are joined by an edge if ...
- 19.3k
35
votes
5
answers
3k
views
A Queen and her Pawns
Place a queen and as many pawns as possible on a chessboard so that the queen has just one way of capturing all the pawns in precisely as many moves as there are pawns. Pawns do not move and do not ...
- 19.3k
3
votes
1
answer
441
views
Largest word tree
I was inspired by this awesome puzzle. Here is an image of a word tree borrowed from there:
In a word tree every path from the root to the leaves must form a distinct word. The size of the tree is ...
- 36.3k
18
votes
7
answers
1k
views
Efficient Mowing at PSE
Your task:
Find the most efficient mowing path around the dark green bushes that mows (passes over) all of the grass (light green).
For those who cannot view the image above, there are 9 rows of 16, ...
- 19.4k
5
votes
2
answers
247
views
Robot painting a $K_5$
A robot starts at a node of a fully connected graph of 5 nodes (shown below). Each turn the robot can move across an edge and paint it in one of two colours - blue for odd turns and red for even turns....
- 36.3k
3
votes
2
answers
2k
views
The longest path of edges on a 3x3 grid
A robot is placed on some vertex of a 3x3 grid. At each move the robot can take one step (up, down, left or right) along the edge of the grid to the adjacent vertex, but it cannot go outside the grid. ...
- 36.3k
6
votes
2
answers
802
views
Splitting the integers 1 to 36
Split the integers 1 to 36 into two sets, A and B, such that any number in set A has a common divisor greater than 1 with no more than two other numbers in A, but for every number in B there are at ...
- 19.3k
-1
votes
1
answer
222
views
How to arrange the colored cells in game grid?
Puzzle: In a game grid some cells are missing. Each line has only one colored cell with a label (a number greater than zero). This is an example grid and the number of columns/rows can be less than ...
- 1,701
12
votes
3
answers
2k
views
Longest infinite loop of 5 states
This is based on a question I posed in The Nineteenth Byte:
What group of 5 states have the longest total name, under the constraint that you must be able to travel from one state to another in the ...
3
votes
1
answer
949
views
Most efficient way for people along the edges of a grid to move to the center
I'm considering a $2k\times 2k$ square grid ($k\in\mathbb Z^+$) with $8k$ highly rational people standing along the vertices forming the perimeter. All of these people want to go to the centre of the ...
- 309
2
votes
2
answers
217
views
Powerful Octagon
Place different integers on the vertices of an octagon so that the sum of the integers in any two vertices joined by one of its edges is a power of 2. Do so in such a way that the largest integer used ...
- 19.3k
2
votes
1
answer
130
views
Fetching Alchemist, Excavation I
This is a puzzle in the Fetching Alchemist series. It has been generated especially for Puzzling Stack Exchange.
Please note that, in my opinion, imperfect solutions should be up-voted so long as they ...
- 2,042
0
votes
1
answer
82
views
Fetching Alchemist, Grand Potion I
This is a puzzle in the Fetching Alchemist series.
There's no selling in this puzzle, just one potion to brew, but with a lot of ingredients.
Please note that, in my opinion, imperfect solutions ...
- 2,042
2
votes
3
answers
200
views
Advanced Fetching Alchemist II
This is a puzzle in the Fetching Alchemist series. From now on, you complete quests at the place you start at as well.
Please note that, in my opinion, imperfect solutions should be up-voted so long ...
- 2,042