Questions tagged [optimization]

A puzzle where you have to optimize a certain objective function (maximize profit, minimize cost). There should ideally be a provable best answer, to avoid making the puzzle into an [open-ended] game.

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8
votes
2answers
390 views

Rack 'Em Up! 🎱

In a game of English eight-ball pool, a set of 15 balls are arranged or 'racked' in the shape of an equilateral triangle. In order for the balls to be racked fairly, they must be arranged like so: <...
11
votes
1answer
765 views

How many circles needed to pass through each of 5x5 lattice points?

You are given a 5x5 set of lattice points. What is the minimum number of circles, which pass through each of the 25 points at least once?
6
votes
1answer
320 views

An intriguing game construction

I found that the book "Amusements In Chess," by Henry Ernest Dudney, has been morphed into a website. In the section "Various Chess Puzzles, I came across this particular puzzle that ...
3
votes
3answers
192 views

Footmen and Friends #4: Double Iced

It's time for Episode 4 after a long time off air! This time, it's another unusual dazzle. It's a short, but succulent, sweet New Year's treat. In the starting position, with no pieces other than the ...
4
votes
1answer
157 views

Find the fastest stalemate for Black!

In the below position, how many moves will it take for Black to be stalemated? Black moves first, and both sides are working together. Black's pawns are moving down. Have fun solving! Zdravko Maslar, ...
12
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3answers
919 views

8 soldiers lining up for the morning assembly

There are 8 soldiers, gathering and lining up every morning for their military service. The commander at the head of these soldiers demands that the morning lineup of these soldiers be arranged ...
11
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4answers
956 views

Consecutive captures on the same square

What is the most number of consecutive captures that you can have on the same square in a standard game of chess? Assume that black and white alternate in taking turns. Good luck!
0
votes
1answer
169 views

Selfmate In How Few? #2-Taking Flight

After my first one was solved so quickly, it's time for the next meal! It's another one that I created for the same mentioned site. Warning: this is a fairly long one, even with its simple strategy! ...
10
votes
4answers
2k views

Make 38 using the least possible digits 8

This is a follow up question to this one, which was: Make the number 1998 using the minimum amount of digits 8. Your allowed operations are +, -, *, /, ^, % (percent). You need not use only integers ...
6
votes
1answer
318 views

Alice and Bob playing Neighboring Sums Game

Alice and Bob are playing the neighbouring game which is originally single game to get the highest point at the end. You start with an empty 4x4 grid. At each turn you can choose an empty cell and ...
10
votes
1answer
924 views

Is a fake coin lighter or heavier? [closed]

There are 16 coins, 3 of which are slightly heavier or lighter than the others. The counterfeit coins have the same weight but it is not known whether they are heavier or lighter than the genuine ones....
2
votes
1answer
124 views

Selfmate In How Few? #1

Here's a new idea that I had. Instead of giving you the number of moves, you must find it yourself! Of course, the problems must be clear and concise. Now, let's get started! For the first one, here ...
5
votes
4answers
455 views

Most Captures Chess

In Most Captures Chess puzzle, you will need to provide a legal game where it is Blacks to play and where they have the most different ways to capture a White piece. For instance, the next game allows ...
0
votes
1answer
132 views

How many roads in a Tak square?

The board game Tak is played on a chess-like board of variable size (most commonly, 5x5 and 6x6). Players place and move pieces on the board with the goal of creating a "road", which is a ...
7
votes
4answers
818 views

Neighboring sums 5x5 game

You start with an empty 5x5 grid. At each turn you choose an empty cell and place a value in it. The placed value is given by the following rules: If the chosen cell has no neighboring (horizontal or ...
11
votes
4answers
996 views

Neighboring sums 4x4 game

Here is an interesting game. You start with an empty 4x4 grid. At each turn you can choose an empty cell and place a value in it. The placed value is given by the following rules: If the chosen cell ...
5
votes
3answers
333 views

Optimal Strategy for Matching Pairs

I found a reality TV show recently that I thought would make a fun puzzle. On the show are 10 men and 10 women that have been "matched by experts" (ie. randomly paired). Their goal is to ...
4
votes
1answer
171 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
764 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 ...
5
votes
3answers
282 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....
18
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
130 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 ...
0
votes
6answers
336 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 ...
10
votes
2answers
511 views

What is the minimum number of problems in the pool? [closed]

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
194 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 ...
10
votes
3answers
585 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
186 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
240 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 ...
25
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
357 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
238 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
1k 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
244 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
222 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
256 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 ...
4
votes
1answer
311 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 ...
2
votes
1answer
280 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
394 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 ...
3
votes
2answers
151 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
189 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
177 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
137 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
180 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
122 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
271 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
1k 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
220 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
111 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
527 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. ...

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