All Questions
Tagged with optimization graph-theory
30
questions
2
votes
1
answer
113
views
Advanced Fetching Alchemist I
This follows the same rules as previous Fetching Alchemist puzzles, except you choose where you start, and you may now return to your starting place after leaving it.
How to Play
You are looking for ...
- 2,042
0
votes
1
answer
144
views
Trail passing through squares of a grid
Let's construct a 10x10 grid. 0n the 100 squares you are allowed to place 7 bases (the red dots in the diagram below) in any square on the grid. Then you fill the grid with skinny trominoes. The ...
- 2,915
1
vote
2
answers
279
views
Minimize the longest King chain on a 6x6 ternary grid
This puzzle is an extension of this one: Minimize the longest King chain on a 5x5 binary board
Given a grid filled with numbers, we define a King chain to be a path on the grid such that:
The path ...
- 36.3k
0
votes
1
answer
178
views
Minimize the longest King chain on a 7x7 binary grid
This puzzle is an extension of this one: Minimize the longest King chain on a 5x5 binary board
Given a grid filled with numbers, we define a King chain to be a path on the grid such that:
The path ...
- 36.3k
13
votes
7
answers
980
views
Minimize the longest King chain on a 5x5 binary board
Given a grid filled with numbers, let's define a King chain to be a path on the grid such that
the path can be traversed with chess King's moves (moving to one of 8 adjacent cells at a time),
the ...
- 16.3k
8
votes
1
answer
339
views
Four color a map - but go light on the fourth color!
Here's a map, which I found here:
Your challenge is to four-color this map while minimizing your use of the fourth color.
More specifically, color the map with four colors so each region is a ...
- 7,158
8
votes
3
answers
406
views
What is the minimum count of steps required to complete this dominoes maze?
Here's a map:
How to play
Legend:
(◾) = Start point
★ = Objective
⚑ = End point
Mission: ...
- 964
6
votes
7
answers
329
views
Find minimum number of meeting periods to reach 2 degrees of separation for a group [closed]
I am running a training course and I want to arrange a set of 1:1 meeting periods between the participants such that at the end of the day there is a maximum of 2 degrees of separation between any of ...
- 69
2
votes
2
answers
377
views
Scheduling Meetings
I came across this problem in real life and thought it could be made into an interesting puzzle. I will enjoy seeing how my eventual solution could be improved!
Here's the situation.
There ...
- 23.7k
3
votes
1
answer
485
views
8 Train Stations
You are going to build $8$ train stations and the railroads with it in an area. But you are asked to build these stations and their railroads in a very efficient way where there has to be the least ...
- 30.4k
8
votes
1
answer
469
views
A perfect metro map
You are working for a company and asked to create a perfect metro map where there will be as many stops as possible. But there are two constraints which limits the number of tracks (railroads) and ...
- 30.4k
18
votes
5
answers
1k
views
Maximize the number of paths
You have exactly 990 edges. Assemble them into a simple undirected graph with two distinguished vertices A and B, such that the number of different simple paths from A to B is as large as you can make ...
10
votes
1
answer
665
views
Building a cheap road
The governor of Reniets (a land far, far away!) is known to be very stingy.
He has to build a road which connects all the five cities in the region, which are oddly arranged on the vertices of a ...
- 12.6k
10
votes
5
answers
966
views
Houses in a grid
You are a city planner tasked with the placement of unit-square-sized houses in a rectangular-grid allotment, the size of which is up to you but must be as small as possible to save money. The number ...
- 526
12
votes
3
answers
1k
views
Dissecting a square
You are asked to dissect an $N \times N$ square into polyomino pieces such that each piece shares a portion of its boundary with exactly $D$ other pieces, and no piece has area exceeding $N$. This can ...
- 4,400