Questions tagged [optimization]
A mathematical puzzle where you have to optimize a certain objective function (maximize profit, minimize cost).
380
questions
3
votes
1answer
112 views
Day-in-the-sun chess
Inspired by this puzzle: Doubled Knights redux
Let's make the following change to the rules of chess. Every piece can once per game (on its day in the sun) make a double move.
Clarifications:
Things ...
21
votes
2answers
672 views
Amoebas escaping the prison
There is an infinite grid of squares.
In one of the squares, there lives an amoeba (marked as a circle in the following pictures).
Amoebas cannot move, but they can perform their unique action: an ...
3
votes
3answers
199 views
A tribute to “Most ways to uncheck the king”
Today, we had the great privilege to see @Paul Panzer's answer being ticked at @thesilican's absorbing puzzle.
I here propose a variant of his puzzle where it's not mandatory to use a legal chess game....
16
votes
4answers
2k views
Most ways to uncheck the king
Here's my attempt at a chess puzzle
Your task is to construct a legal chess position where:
It is black's turn to move
Black is in check
Black has the greatest number of different legal moves ...
-4
votes
1answer
84 views
Use only πs to get e
I am taking this puzzle from inspiration from the Four Fours to get Pi puzzle. The puzzle rules are just slightly different. Here are the rules:
You are trying to get as close to e as possible with ...
1
vote
6answers
271 views
Move 3 matches to maximize triangles
The problem is as follows:
The figure from below shows 9 matches. If only 3 of them are changed
from their positions, then what is the most number of triangles that can be
made?
The alternatives ...
9
votes
2answers
425 views
What is the minimum number of problems in the pool?
Using a pool of problems, 16 tests will be formed, following certain conditions:
Every test should have the same number of problems.
Any problem should be included in at most 8 tests.
Every group of ...
7
votes
1answer
158 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 ...
9
votes
2answers
349 views
Optimal refueling strategy
On the way home from work, I want to refuel my car. There are 5 petrol stations along the way that all have a different price for petrol. I know that the prices will be in the range [A, B], chosen ...
5
votes
2answers
145 views
Switching Black and White
In this Chess puzzle, your aim is to switch black and white, with a legal game, and arrive at the final position:
This aim is likely unreachable. So you must try to get the maximum number of pieces ...
2
votes
1answer
189 views
Lasers: (Rotation + Movement) (Level 4)
Previous Level: Lasers: Cross through the bridges (Level 3)
Here's another level for my new puzzle, after a long time. Some new ideas came too:
Rules:
There will be lasers which are shaped like an ...
24
votes
6answers
3k views
Chess solitaire: The King's longest walk
Challenge: maximize the number of moves white needs for its king to reach a square of your choosing, adhering to the following rules:
Black does not move
Like normal: The king may not be in a ...
6
votes
2answers
311 views
Fastest draw from opening position in chess
When playing a normal game of chess, assuming the opponents are cooperating:
In how many moves can a draw be unavoidable, excluding voluntary draws or draws by repetition of moves?
1 While not ...
8
votes
1answer
203 views
Generalized color balls in a 4x4 grid
This is a generalization of the Colored balls in a 4x4 grid puzzle that was proposed by Darrel Hoffman.
Colored balls from 4 different colors are placed in a 4x4 grid. There is at least one ball from ...
8
votes
4answers
948 views
Colored balls in a 4x4 grid
Colored balls are placed in a 4x4 grid. A move consists of swapping two adjacent (horizontally or vertically) balls. What is the least number of moves required to form 4 connected components*, one for ...
4
votes
1answer
215 views
Most 5s in a 5x5 Super Minesweeper grid
In a Super™ Minesweeper grid each cell is either a mine or a value. A value in row $𝑟$ and column $𝑐$ represents the total number of mines located in row $𝑟$ or column $𝑐$.
What is the most number ...
6
votes
1answer
178 views
7-QWERTY-distance words
My previous puzzle The QWERTY-shortest word was solved nearly instantly by the effective puzzling community. I also believe it is because the main parameter of the puzzle 4.7 was not perferectly set. ...
3
votes
1answer
195 views
Lasers: Cross through the bridges (Level 3)
Previous Level:- Lasers: The Reflection (Level 2)
Rules :
There will be lasers which are shaped like an arrow. The arrows pointing in the respective direction shows where the laser goes and the ...
3
votes
1answer
219 views
Lasers: The Reflection (Level 2)
Previous Level:- Lasers : Introduction (Level $1$)
So here is my lasers level 2 continued, and I have something new, mirrors!
Rules:
There will be lasers which are shaped like an arrow. The arrows ...
1
vote
1answer
195 views
Lasers : Introduction (Level $1$)
Lasers is a new type of puzzle I created. (Taken help from this example, The Lazy Laser Physicist: Part 2)
There will more ideas to come too, and they will be a bit simple yet different.
Rules :
...
9
votes
2answers
346 views
Maximize my flags
You are given the next list of 48 flags.
For each pair of flags that are side by side, you score 1 point per color they share as a frontier. For instance France and Finland score 1 point thanks to ...
2
votes
2answers
128 views
Presidential Election
This puzzle was inspired by the current 2020 US presidential election.
You are running for president in a country with 10 states. To win a state you must conduct more rallies than your opponent. ...
3
votes
1answer
175 views
Fewest number of weighings to check if coins are correctly labelled
This is inspired by the following question over at Computer Science Stack Exchange: Information-theoretic limits for a weighing puzzle
You are given 11 coins with labels 1, 2, 3, ... up to 11. You ...
0
votes
1answer
144 views
Fill grid with Bs
Here is a letter grid:
Here are the rules as to how to manipulate the letters in the grid:
A marker starts at the first square.
For each move you can move the marker one square either up, down, left ...
1
vote
1answer
119 views
Minimum moves to lose grid game
Here is a number grid:
And here is the rule for how to move:
A move consists of selecting two adjacent squares (either vertically, horizontally or diagonally) and dividing the sum of the two numbers ...
6
votes
1answer
154 views
Reassemble NaNoWriMo
Today is the start of NaNoWriMo (National Novel Writing Month), and I wanted to come up with some type of a puzzle to celebrate. I think this is a new style of puzzle (if it's not, please let me know!)...
2
votes
1answer
100 views
How to find the least amount of helpers required to complete a voyage?
The puzzle is as follows:
Vincent is a scientist and is about to begin a journey in Antarctica,
as he must reach his laboratory at the next station. However, the only
buggy available at the base ...
9
votes
1answer
235 views
Minimum number of moves to win this number game
This puzzle is inspired by this puzzle that I answered: Is equality possible?
Here is the number grid from that puzzle:
And here is the rule for how to move:
A move consists of selecting two ...
7
votes
2answers
980 views
The Popular Letter Chessboard
You are given a Chess board with black and white squares.
You must fill your Chess board with Merriam Webster English words, or other equivalent dictionnaries if you prefer such that each square ...
4
votes
1answer
179 views
Kings' Chess Harem
Pursueing these two related puzzles, Chess Bloodshed and Devouring Nobility I create for you Kings' Chess Harem where you have to find, with the minimum number of moves, a legal game where all pawns ...
10
votes
2answers
1k views
Chess Bloodshed
This puzzle is the idea of Dmitry Kamenetsky in a comment of my puzzle Devouring Nobility.
Find, with the minimum number of moves, a legal game where all pieces are captured except the two kings.
1
vote
1answer
94 views
Does a way to find the least amount of pizza cuts for a certain number of slices (11) exist?
I found this problem in a Logic and Reason book from 2000's which seems to be reprinted or adapted from Martin Gardner's book of recreational puzzles. In the beginning it seemed rather easy but I ...
8
votes
2answers
504 views
Devouring Nobility
Provide, with the minimum number of moves, a legal chess game where all pieces are captured except the sixteen pawns and the two kings.
Example of final configuration:
Which is done in 21 moves:
1. ...
11
votes
3answers
576 views
1000 gold coins to share with the knight
Note: This riddle is similar to this riddle: 1000 gold coins to share with the king, except now YOU are the king, and the rules are switched up a bit. And the situation is wackier...
You are the King ...
5
votes
1answer
197 views
The QWERTY-shortest word
For this puzzle, I define the distance between two letters as the shortest way on a QWERTY keyboard to go from a letter to another with a path.
Examples:
Q and W are seperated by a distance of 1.
2 ...
26
votes
4answers
3k views
1000 gold coins to share with the king
You are the knight of a great kingdom in an unknown world. Your king sent you to a dungeon and you killed the dragon and got 1000 gold coins from the dragon’s lair. Normally, you are supposed to give ...
12
votes
0answers
440 views
Qubes: Oh, For the Love Of
TL;DR: This is a mixture between a tribute/spin-off puzzle and an attempt at a new puzzle type, greatly inspired by the notorious arcade game, Q*bert, published originally by Gottlieb Amusement Games. ...
3
votes
1answer
177 views
Create the freest arrangement of white chess pieces on board by consequently moving your pieces
You start with this board. You're the White. Freedom Index of initial arrangment of your chess pieces is equal to 20 (each pawn has two moves, each knight has two moves)
Your goal is to have as much ...
1
vote
1answer
94 views
Minimise battle time in Monster's Den
So there is this excellent flash game, Monster's Den. In order to make a high score, I must complete many battles..this question is about battles with the Legendary Monsters.
The target is to reduce ...
7
votes
4answers
415 views
Buying weight plates for a home gym, what is the fewest number I need
I'm buying a home gym set-up for my son (really!) and I want to know the fewest number of weight plates I need to buy to be able to go up in 5kg increments to 170kg. The bar weighs 20kg and the ...
2
votes
1answer
171 views
Lazy Box Sorting
In front of Louis there are 10 boxes containing different foods: tomatoes, (red) herrings, and bananas.
The boxes are arranged side by side in a line. Right next to the last box are three bigger ...
-1
votes
2answers
102 views
The Range of Taxi Fares [closed]
You are in the back of a NYC taxi, and know exactly how fare your trip was in miles (m), and exactly how long it took in hours (t). The taxi driver gives you bill, but you want to make sure they've ...
2
votes
3answers
336 views
Can you minimise the arithmetic average?
Let $n$ be a positive integer. There are $2n$ $1$s written on the whiteboard. John repeats the following procedure $3n$ times, as follows:
Choose two numbers $x,y$ on the board, then replace each of ...
9
votes
7answers
1k views
Weights on a binary tree
If for a given binary tree:
Every node with 2 children has a weight of 3
Every node with only 1 child has a weight of 2
Every node with no children (a leaf) has a weight of 1
The weight of a binary ...
3
votes
1answer
161 views
Shuffling Magnets
For an experiment, I have to place magnets onto a rectangular board whose dimensions are 3 and 3.5 inches. Between each phase of the experiment, I have to shuffle these magnets around, but if two ...
7
votes
3answers
297 views
Touching triangles at their vertices
What is the minimum number of non overlapping congruent triangles arranged in the plane,
such that each vertex of the triangles coincide with exactly three triangles?
8
votes
2answers
420 views
Modifying the puzzle: Cooperative hat-guessing, no mistakes, 3+ colors
Following Guess your hat color, but you don't have to and it's interpretation via Covering codes I tried to create a puzzle with more hat variativity, i.g. 3 types of hats.
4 hats are put on 4 ...
8
votes
3answers
480 views
Guess your hat color, but you don't have to
Here is the puzzle:
N hats are put on N logicians, each hat color is selected randomly: black or white.
As usual, every logician doesn't see the hat on his own head, but sees the rest. They cannot ...
5
votes
1answer
123 views
Competitive puzzles
Do you know any sort of puzzles that can work in the context of a short competition? In other words, puzzles that have these features:
The premise should be fairly simple to follow (but the solution ...
13
votes
2answers
801 views
A tournament, and a tight personal schedule
A 64-player binary tournament bracket is about to start. You plan to free up your schedule in advance to watch some of the matchups (meaning, you can plan to watch the second semifinal, for example, ...
