All Questions
21
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 ...
- 3,323
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
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
6
votes
2
answers
814
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
224
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
3
votes
1
answer
951
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
218
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
132
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
83
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
201
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
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