Questions tagged [optimization]

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

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1
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2answers
156 views

How many lines are needed to connect all smiling toasters in a 4x4 grid?

The puzzle is as follows: How many straight lines do you need to draw the least possible to join all the smiling toasters if you should not raise the pen or go over any line already drawn? Remember ...
1
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2answers
233 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 ...
0
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1answer
128 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 ...
5
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0answers
194 views

Choosing squares on a square board [closed]

I have an $8 \times 8$ board. On the board, I want to choose 2 unit squares in each column and row such that none of the chosen squares are touching. This means they cannot share a side or a corner. ...
4
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1answer
146 views

Chess - I will eat!

Suppose that you are playing White, and your aim is to eat a black piece (pawns qualitfy) in the fewest moves as possible and Black are not cooperating at all, and, even more, Black's aim is to ...
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2answers
114 views

How to find the least number of extractions to make the word QATAR?

The riddle is as follows: A local library has lended its catalog card cabinet so it can be used in a raffle. The raffle prize is a luxurious travel to the Middle East for vacations to an employee ...
3
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2answers
497 views

Matches to move in order to get right roman numeral over fifty

The riddle is as follows: The figure from below represents a set of roman numerals wrote in such a way that the sum is not correct. The numbers are arranged as: 50+12=51 How many matches minimum ...
14
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5answers
1k views

Shooting them blanks (double optimization task)

I don't know the answer, I just state that this problem could be interesting. Best estimate gets the tick. "Battleships" game field (at least, in the USSR version I used to play) is a 10x10 ...
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0answers
97 views

Selfmate In How Few? #3-Unknown Limits

I dug up the below old position when going through a Google Docs document today. I know that it's supposed to be a somewhat winding, clearly dualed, selfmate. To be honest, I genuinely don't know the ...
13
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7answers
846 views

Minimize the longest King chain on a 5x5 binary board

Given a grid filled with numbers, let's define a King chain to be a path on the grid such that the path can be traversed with chess King's moves (moving to one of 8 adjacent cells at a time), the ...
10
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1answer
844 views

How many queens so every unthreatened vacant square traps a knight?

How many queens does it take at minimum to occupy an empty chess board, so that whichever vacant and non-threatened square you put a knight on, the knight won't have a square to go to that is not ...
10
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2answers
463 views

Sixteen chess pieces on a square board

It is well known that the eight main chess pieces cannot cover a chess board. Suppose I have two sets of the eight main pieces. What is the size of the largest chess-like square board all of whose ...
5
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1answer
176 views

Anti-Chess Squares

Playing regular rules for both white and black try to eliminate all the square formations by black and/or white. From the above starting setup all rooks form a square. Also white's queen rook pawn, ...
4
votes
1answer
101 views

How many queens are needed to attack all white squares?

This question: How can 3 queens control the white squares? got me thinking... What is the fewest number of queens needed to attack every white square? Rules: Only queens allowed Every white square is ...
14
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2answers
2k views

Three queens and two rooks covering the chess board… again!

Three queens and two rooks can be placed on a chess board so that all empty squares are under attack, as has been shown here: 3 queens and 2 rooks covering a 8x8 chess board. What if we require that ...
7
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2answers
905 views

21 knights covering a 11x11 chess board

Can you place 21 knights on a 11x11 chess board, such that every empty cell is under attack? Good luck! Here is a similar question for 10x10: Knights covering a 10x10 chess board
3
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2answers
202 views

Determine minimal number of moves to find cells on a square table 10×10 in which a treasure is hidden

In a 10x10 square table, two neigbouring 1x1 cells contain a hidden treasure. John needs to guess these cells. In one move he can choose some cell of the table and can get information whether there is ...
2
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1answer
186 views

Piercing Bullets

Under 30-secs. bullet time control the above position results after n moves. What is the fewest number of moves possible?
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1answer
100 views

Fun with Letters, Words and Sentences? [closed]

I have a game, but first, I need to explain how it works. Take a sentence, completely meaningful. Suppose the sentence is, "Yes, yesterday we ate the meal sometime at night". In this ...
6
votes
2answers
459 views

Covering a 15x15 grid with rectangles

You are given a 15x15 grid and asked to cover it with rectangles whose dimensions are a power of 2. For example you can use rectangles 8x1 and 4x4, but not 2x3. The rectangles must cover every cell of ...
30
votes
5answers
5k views

How can 3 queens control the white squares?

It is well known that there is no way of arranging 4 queens on a checker board in such a way that every square is occupied or threatened. Now consider a slight variation where we only need to cover ...
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votes
2answers
118 views

maximum product of n positive integers whose sum is k [closed]

We have to find n numbers such that $$ x_1 + x_2 + \cdots + x_n = k $$ $$ x_1 * x_2 * .....* x_n = maximum $$ What are the values of $x_1, x_2...x_n$ ? Note that $x_1, x_2...x_n$ are all positive ...
4
votes
4answers
613 views

maximum product of n numbers whose sum is k [closed]

We are given two numbers, n and k. We have to find n numbers such that $$ x_1 + x_2 + \cdots + x_n = k $$ $$ x_1 * x_2 * .....* x_n = maximum $$ What are the values of $ x_1, x_2, ...x_n$ if these ...
2
votes
4answers
202 views

The Greenhouse Problem version 2

This is an extension of Nilster's great puzzle: The Greenhouse Problem The task is the same, but this time sprinklers cover only a 3x3 square around them. For completeness, here is the full set of ...
15
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4answers
1k views

The Greenhouse Problem

While I was playing a certain popular indie farming game, I came across a dilemma. I have a greenhouse that I'd like to fill as efficiently as possible. How many plants can I fit in the greenhouse? ...
4
votes
3answers
176 views

Experts at failure

Construction challenge: Find a position with the longest sequence of unique losing moves, i.e. white to move has one and only one move that will lead to a lost (for white) position. White makes this ...
8
votes
1answer
517 views

Doubly Pure Checkmate

A pure checkmate is a checkmate where for each square the king might go to, there’s exactly one reason it can’t. The famous Légal mate is one example, so is a KR vs K checkmate. What’s the minimum ...
1
vote
1answer
123 views

Mirror Mirror On The Board

Mirror mirror in the board Decipher the riddle of this horde How many moves to it, please? To put my brain at ease! Both sides help, follow their paths The solution you must craft Oh, and there is but ...
1
vote
2answers
103 views

A number built with two-digit primes

What is the largest number, which can built as a sequence (from left to right) of different two-digit primes only? For example, 1371731 is valid, 137131 is invalid (containing 13 twice), 139717 is ...
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1answer
108 views

How to open the lock from this safe?

The puzzle is as follows: The figure from below shows a lock mechanism used to store sensitive data microfilms from a certain lab. This mechanism is magnetic and consists in numbered buttons which ...
4
votes
4answers
372 views

How to get the least number of flips to a plastic chips to get a certain figure?

The puzzle is as follows: (Transcription with grammar errors fixed) A game consists of the following: The challenge is to flip the chips in such a way so that they are as in state 2. You start in ...
4
votes
2answers
175 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 ...
2
votes
3answers
160 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 ...
0
votes
2answers
130 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
368 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
732 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
249 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
votes
3answers
177 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
145 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
891 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
928 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!
1
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0answers
110 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 ...
4
votes
1answer
271 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
849 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
vote
1answer
102 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 ...
0
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0answers
38 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
votes
4answers
440 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
123 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
790 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 ...

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