Questions tagged [optimization]

A mathematical puzzle where you have to optimize a certain objective function (maximize profit, minimize cost).

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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
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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
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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
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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
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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
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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 ...
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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, ...

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