Questions tagged [optimization]

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

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7
votes
2answers
167 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
44 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 ...
4
votes
3answers
161 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
244 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
58 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
340 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
142 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
585 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
0answers
122 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
85 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
431 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
72 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
635 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
375 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
256 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
957 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
254 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
397 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
174 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
258 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
122 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
482 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
99 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
205 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
229 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
151 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
229 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
126 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
192 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
139 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
94 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
838 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
votes
1answer
839 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
votes
2answers
458 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
votes
1answer
172 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
98 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
votes
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
votes
2answers
900 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
votes
2answers
196 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
votes
1answer
181 views

Piercing Bullets

Under 30-secs. bullet time control the above position results after n moves. What is the fewest number of moves possible?
-5
votes
1answer
98 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
452 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 ...

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