Questions tagged [optimization]

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

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4
votes
2answers
154 views

Maximum number of kings that can exit

N kings are placed on a chessboard, with at most one king on any square. Following standard rules of movement (one square in any direction), every king must be able to reach some edge of the board ...
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3answers
149 views

Maximum number of triangles formed in a pentagon with equal area

All diagonals of a convex pentagon are drawn, dividing it in one smaller pentagon and 10 triangles. Find the maximum number of triangles with the same area that may exist in the division. The best I ...
-3
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0answers
109 views

Square grids with letters [closed]

Let's have a 7x7 letter square grid. In every row, column, and diagonal, the same letter is not allowed to appear twice. What is the maximum number of words that such a square grid can contain? Words ...
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2answers
123 views

How do you find the perimeter of a set of odd looking squares and triangles?

The problem is as follows: The alternatives given in my book are: 76 cm 80 cm 92 cm 100 cm Upon the first inspection. I'm getting the idea that I have to make a system of equations. Assuming that ...
8
votes
2answers
342 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
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1answer
689 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?
5
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0answers
156 views

An intriguing game construction

I found that the book "Amusements In Chess," by Henry Ernest Dudney, has been put onto the web in the form of a website. In the section "Various Chess Puzzles, I came across this ...
3
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3answers
142 views

Footmen and Friends #4: Double Iced

It's time for Episode 4 after a long time off air! This, it's another unusual dazzle. It's a short, but succulent, sweet New Year's treat. In the stating position, with no pieces other than the kings, ...
5
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1answer
131 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
861 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
897 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!
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0answers
104 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
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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 ...
4
votes
1answer
261 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
802 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....
1
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1answer
97 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 ...
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0answers
37 views

Rotating through a word [duplicate]

Take the word no if you move the first letter to the end you have a new word on I consider that 1 rotation. What is the largest word that can be fully rotated, the most number of rotations?
5
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4answers
408 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
121 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
770 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
934 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
266 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 ...
3
votes
1answer
125 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
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2answers
708 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 ...
4
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3answers
249 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....
19
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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
109 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 ...
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6answers
288 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
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2answers
495 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
163 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
530 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
157 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
207 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 ...
26
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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
318 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
207 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
956 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
220 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
182 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
216 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
239 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
241 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
357 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
131 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
177 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
150 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
121 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
159 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
105 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
240 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 ...

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