Questions tagged [optimization]

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

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6
votes
1answer
248 views

Discounts in a shop

I came across this sign in a shop and thought it could make a nice puzzle. So you can buy items and get discounts depending on how many items you got. You can combine discounts and use as many as you ...
13
votes
6answers
1k views

What is the minimum number of helpers that an explorer need to cross the desert?

There is a desert which can be crossed only by walking and this takes six days. The explorers of the desert can carry at most four days' water and food. If they want, they can take helpers with them. ...
4
votes
1answer
81 views

Mix a 2x2 Rubik’s cube

What is the minimum number of 1/4 turns of a solved 2x2 Rubik’s cube, such that no face will have two tiles of the same color? (I do not have this puzzle’s solution.)
1
vote
1answer
139 views

Catch the fugitive

The fugitive is at the origin. He moves at a speed of 100. You have a guard at every integer coordinate except the origin. A guard's speed is 1. The fugitive and your guards move simultaneously and ...
5
votes
3answers
214 views

The vaccine distribution conundrum

The context is that of a pandemic that is spreading wildly and requiring global vaccination of the population. You are working in a distribution center for the vaccines. One day you have been ...
19
votes
1answer
1k views

Beans under the chessboard

Under every grid cell of a chessboard, I put either one bean or nothing. Now if you choose a (grid) rectangular area on the chessboard, then I will tell you the parity of the number of beans under ...
2
votes
1answer
98 views

Fetching Alchemist, Excavation I

This is a puzzle in the Fetching Alchemist series. It has been generated especially for Puzzling Stack Exchange. Please note that, in my opinion, imperfect solutions should be up-voted so long as they ...
0
votes
1answer
69 views

Fetching Alchemist, Grand Potion I

This is a puzzle in the Fetching Alchemist series. There's no selling in this puzzle, just one potion to brew, but with a lot of ingredients. Please note that, in my opinion, imperfect solutions ...
2
votes
3answers
191 views

Advanced Fetching Alchemist II

This is a puzzle in the Fetching Alchemist series. From now on, you complete quests at the place you start at as well. Please note that, in my opinion, imperfect solutions should be up-voted so long ...
2
votes
1answer
97 views

Advanced Fetching Alchemist I

This follows the same rules as previous Fetching Alchemist puzzles, except you choose where you start, and you may now return to your starting place after leaving it. How to Play You are looking for ...
10
votes
2answers
554 views

Adding coins inside a ring of coins

17 identical coins with diameter 1 are lying flat on a table, such that their midpoints build the vertices of a regular 17-gon (regular heptadecagon) and adjacent coins touch each other. What is the ...
1
vote
0answers
49 views

Grids with tiles of two colors and connectors

Make a square grid with an even side. Make a continuous trail which passes through all small squares; the trail ends where it started. Where there is an angle you can put a red or a blue tile. On ...
5
votes
3answers
165 views

Numbers with minimal sum at the vertices of a cube

The eight vertices of a cube are marked with numbers from 1 to 8 such that the sum of any three numbers on any face is not less than 10. What is the minimum sum of the four numbers on a face?
4
votes
1answer
64 views

A 4x6 grid with adjacent integers with gcd > 1

You are given a 4x6 square grid. Each square of the grid should be filled with different positive integers. The gcd (greatest common divisor) of any two adjacent (horizontally or vertically) squares ...
3
votes
3answers
251 views

Not selling 100 pencils

A shop sells pencils only in boxes of fixed size. It cannot sell 100 pencils. It can sell any larger amount of pencils. It has one of each size box on display. question 1: What is the minimum amount ...
3
votes
1answer
62 views

Divisors ending with digits 0-9 each

What is the smallest positive integer, which has - for each of the digit 0-9 - a divisor ending with this digit?
8
votes
5answers
1k views

Minimize 1×3 tiles on a 5×5 table to block any more 1×3 tiles

What is the minimum number of 1×3 tiles that can be put on a 5×5 table so that no more 1×3 tiles can be put on it? Borders of a tiles are parallel to sides of the table. It is 5 but I can not prove ...
2
votes
2answers
345 views

Traffic light controller

Consider the following diagram. Once every 2 seconds a car enters from the top and travels down towards the exit. Once every 3 seconds a car enters from the left and travels to the right exit. In the ...
9
votes
1answer
145 views

Interchanging knights and rooks… again!

Is it possible to interchange the positions of the the two black knights and two black rooks with those of the two white knights and two white rooks? Movements allowed are those of the corresponding ...
10
votes
2answers
590 views

Two football teams

Twenty two football players have agreed to split every week into two teams and play a match against each other. Every week, teams will be chosen differently, 11 players in each team, and they will ...
5
votes
1answer
230 views

Looking for Navigators for the Famous Vega Classic

Do you have what it takes to compete in the famous Vega Classic? Looking for skilled navigators. Apply below. You have a craft that is capable of 10m/s$^2$ acceleration in any direction, and we're ...
0
votes
1answer
87 views

Trail passing through squares of a grid

Let's construct a 10x10 grid. 0n the 100 squares you are allowed to place 7 bases (the red dots in the diagram below) in any square on the grid. Then you fill the grid with skinny trominoes. The ...
8
votes
2answers
435 views

Most Complicated Illegal Partial State of Rubik’s Cube

This puzzle is a follow-up for Does The Rubik’s Cube In This Painting Have A Solved State? What is the most complicated illegal “partial state” possible for a Rubik’s Cube? To be more specific: a ...
1
vote
1answer
75 views

How to arrange a set of cubes to get a tower of two?

The puzzle is as follows: Assume that you have this peculiar toy. This toy is composed by many plastic pieces which is shown in the figure from below, all of them are cubes. You can use as many as ...
10
votes
2answers
643 views

Never kill your king … without first seeking proper legal advice!

This is a follow-up to (Almost) all hands on check by @loopy walt. The task (mate in one with as many essential pieces as possible) stays the same, but you are to go about it more cunningly. Recap of ...
7
votes
4answers
2k views

How can you get 13 pounds of coffee by using all three weights each trial?

The puzzle is as follows [with minor copy edits for grammar]: A merchant has a kiosk nearby our market. He has a sack of 52 pounds of coffee to sell. Assuming that he only uses a two pan scale and ...
4
votes
2answers
376 views

Maximum number of masses you can weigh given 3 weights

The puzzle is as follows: Assume that you have a two pan scale and three weights, one of 1 pound, the other 3 pounds and the last one 9 pounds. In only one weighing trial, how many objects of ...
0
votes
1answer
61 views

How can you use a two pan scale to find which coin is counterfeited? [duplicate]

The puzzle is as follows: Detective Mike has four bags with 100 coins of one cent each. All of these coins have the weight with the exception of one coin which weighs a little less than the rest ...
2
votes
1answer
259 views

Arrange candies without repeating pattern

The following puzzle had been posted before but I couldn't understand the only answer that was given there, which was by @neodne . So, I created this post asking someone to explain neodne's answer to ...
8
votes
3answers
959 views

(Almost) all hands on check

Historical note (skip if you like): In this interesting puzzle @TSLF asks for the "maximum number of black and white pieces that are involved in a checkmate position". Originally, they left ...
5
votes
1answer
255 views

Four queens on public transport

The enlightened but, sadly, fictional country of Switzerland has it all: A strong democracy that resists centralism, a reliable public transport network and its own version of chess. Swiss chess ...
6
votes
3answers
400 views

Proving by weighting

Here is the puzzle: Alice and Bob leave in a world where all diamonds are divided into 2 types: Light and Heavy. All diamonds look exactly the same. All light diamonds weight exactly the same, all ...
0
votes
2answers
177 views

Nested six-point stars: least number of cuts to dissemble

The puzzle is as follows: The figure from below represents a peculiar structure which consists in congruent triangles whose sides intersect and is made of an iron wire. How many cuts passing through ...
1
vote
2answers
259 views

Least cuts to get 44 rods from a metal grid

The puzzle is as follows: Suppose that you have a metal structure made by brass wire. Assuming that you must get 44 rods of the same size each. What is the least cuts to be made using an electric ...
1
vote
1answer
124 views

Minimum cuts to make a rectangle into a square, allowing bending

The puzzle is as follows: Mike has a thin sheet of cardboard which is 96 centimeters large by 24 centimeters wide and a guillotine whose maximum cut length is 80 cm. Assuming this guillotine can cut ...
5
votes
1answer
485 views

Chess - Knight Mate

What is the fastest, in terms of moves, for a legal game to come to a checkmate, either black or white with a Knight and such that both all other cases of the checkmated King are attacked by an ...
-2
votes
1answer
100 views

Vowels, consonants and Mathematical Shapes

Your aim is first to select at least three different mathematical shapes. For instance, you could select "a losange", "a disk" and "two lines". You must then ensure that ...
12
votes
1answer
206 views

Three white queens, two white knights, and one rook on a chess board

On an 8 x 8 chessboard, place three white queens, two white knights, and one white rook so that every cell of the board is under attack by at least one piece not standing on it. Source: https://www....
12
votes
4answers
2k views

How many matchsticks need to be removed so there are no equilateral triangles?

The puzzle is as follows [with minor copy edits for grammar]: By only using matchsticks of equal length a set of equilateral triangles has been built as indicated in the figure from below. With that ...
5
votes
1answer
233 views

How to get the least possible sum in a closed loop set of squares?

The puzzle is as follows: The figure from below represents a set of 12 squares joined forming a closed loop. By using only the numbers from 1 to 12 fill in the blanks. The condition is that, without ...
1
vote
2answers
152 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
vote
2answers
231 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
votes
1answer
127 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
votes
0answers
193 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
votes
1answer
141 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 ...
-1
votes
2answers
113 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
votes
2answers
493 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
votes
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 ...
2
votes
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
votes
7answers
841 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 ...

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