Questions tagged [optimization]

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

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70
votes
15answers
67k views

A camel transporting bananas

A somewhat well-known puzzle is described as such: You have a pile of 3,000 bananas. You wish to transport them to a place 1,000 miles away on the back of a camel; however, the camel can only carry ...
7
votes
4answers
309 views

Largest and smallest hexadecagon with sides $1, 2, 3, \dots,16$

Of all hexadecagons lying in the cartesian plane, all of whose vertices are lattice points, and whose sides are of length $1,2,3,\dots,16$ in some order, which two have the largest and smallest area? ...
5
votes
1answer
99 views

Competitive puzzles

Do you know any sort of puzzles that can work in the context of a short competition? In other words, puzzles that have these features: The premise should be fairly simple to follow (but the solution ...
13
votes
2answers
746 views

A tournament, and a tight personal schedule

A 64-player binary tournament bracket is about to start. You plan to free up your schedule in advance to watch some of the matchups (meaning, you can plan to watch the second semifinal, for example, ...
2
votes
2answers
207 views

Creating the hardest 7x7 maze with special pieces

This puzzle stems from these type of questions by Dimity Kamenetsky. Creating the hardest 7x7 maze Creating the hardest 6x6 maze I wanted to know how the best possible solution would change, if I were ...
8
votes
2answers
1k views

Largest cages Killer Sudoku

Task 1: Find the maximum value of $n$ for which it is possible to create a regular uniquely-solvable Killer Sudoku (9x9) such that every cage has atleast $n$ cells in it. Rules for killer sudoku ...
15
votes
3answers
590 views

Largest and smallest dodecagon with sides $1, 2, 3, \dots,12$

Of all dodecagons laying in the cartesian plane, all of whose vertices are lattice points, and whose sides are of length $1, 2, 3, \dots,$ and $12$ in some order, which two have the largest and ...
7
votes
2answers
625 views

Lock Optimisation

In a simple combination lock, a sequence of several digits is used as a password, with one wheel per digit. Generally, it is not possible to unlock the lock without knowing the password, but due to ...
12
votes
5answers
2k views

Maximise your gold!

You met a genie. He gets $150$ magic lamps out, which are numbered from $1$ to $150$. You have to colour each lamp red or blue. After colouring, the genie will count the number of triples $T$ of magic ...
7
votes
2answers
666 views

A Covid-19 puzzle: Alcohol for your School!

You are the principal of a primary school in HK. Schools are resuming soon, and you have to ensure that your school have enough alcohol. Each of the 30 classrooms should have a bottle containing 500mL ...
9
votes
3answers
629 views

Knight and Knaves Castle

I was pretty bored in the lockdown so I thought up a mathematics puzzle, which I haven's solved yet, so the community can solve together. Let $n>1$ be a positive integer. There is a square castle ...
1
vote
1answer
155 views

Optimize a wheel of fortune

(Taken from a mobile game) You have a wheel of fortune with a total of 30 fields. You start with the following fields (name, size, minimal size, effect): "Diamond Field" (D), size 2, min. size 1, ...
2
votes
1answer
64 views

Is there a strategy for the “2 paths, 1 liar 1 truthful” riddle given an N number of paths, rather than just 2?

I hope this question falls into the correct category. I'm sure the 2 paths , 1 liar and 1 truthful is common, however, is there a general strategy given: There are N-number of doors/paths/or ...
8
votes
2answers
192 views

Black Cavalry Fork Attack

On this chess optimization puzzle, there are only black knights and white queens. Your aim is that no black knight is threatened and to maximize the total number of queens the knights could capture. ...
23
votes
2answers
4k views

What if I told you that guessing in Sudoku is very bad and might give you a bad karma?

Yesterday, I tried to solve a regular Sudoku puzzle. Of course, the Sudoku puzzle had a unique solution. But, I was feeling a little lazy, so, rather than solve the puzzle properly, I made guesses! At ...
2
votes
0answers
105 views

Probabilities for “What number is that? — asks grandpa”

Inspired from Multilanguage generalization of "What number is that? Asks Grandpa" and What number is that ? Asks Grandpa In this puzzle we will use the English alphabet of 26 letters. We ...
3
votes
2answers
150 views

Black War Heroes or Whites Save the Queens?

After Black Cavalry successfully captured White princesses, White empire learns their Black opponent is hungry for more and wants White Twin Queens dead! White will never let such a disaster happen ...
4
votes
5answers
187 views

May Make $\frac5{2020}$ 2020

For May 2020, try to create $\dfrac{5}{2020}$ using the least possible number of integers in the set $\{1,3,4,6,7,8,9\}$. $2$, $5$ and $0$ are not allowed. Example: $$\dfrac{4+1}{3\left(673+\frac13\...
8
votes
1answer
240 views

Ways to destroy a Square Matrix [closed]

Sherlock is solving a case where he came across a puzzle. Suppose you are given a square matrix of size $N$, and a gun with Power $F$. Every cell in the matrix is filled with some number, $x$ (...
4
votes
1answer
154 views

The Switchup-2.0

This question from last year has a complete switchup of all non-pawn pieces on the board with all the pawns on the 4th and 5th ranks, The goal was optimize the amount of moves needed to reach the ...
7
votes
3answers
247 views

What is the minimum count of steps required to complete this dominoes maze?

Here's a map: How to play Legend: (◾) = Start point ★ = Objective ⚑ = End point Mission: ...
3
votes
1answer
197 views

Puzzle - Turn all the lights on

A machine has 2020 lights and 1 button. Each button press changes the state of exactly 3 of the lights. That means if the light is currently on, it turns off, and if the light is currently off, it ...
8
votes
0answers
251 views

An Unusual Amount Of Help

Another day, another helpmate to solve! Given that White moves first and to help Black checkmate White, find the least number of moves needed such that Black mates: -With a queen -With a rook -...
2
votes
1answer
121 views

Footmen And Friends #2: Leapfrog

Seeing as the pilot episode was a major success, with an outstanding and correct response from one of our viewers, it’s time for Episode 2. Remember, we show puzzles with kings and pawns only! Those ...
1
vote
2answers
139 views

How can you find the maximum number of cubes when their faces are subsequently painted and placed in a box?

I'm not sure exactly how to visualize this riddle. Can someone help me?. It goes as this: Mike has many identical cubes whose faces are white. He decides to take one of those cubes and places it ...
15
votes
1answer
264 views

The Beehive Clock Maze Puzzle

Here is an example of a maze I'm calling the beehive clock maze: Rules. Let's call the hexes TL, TR, L, M, R, BL, and BR (for top-left, top-right, etc). You start outside and to the left and step ...
14
votes
1answer
929 views

Is this 3d Sudoku possible?

I was looking at images of 3d Sudoku's on Bing, because I was looking for a $9\times9\times9$ Sudoku, where each horizontal, vertical left-right and vertical top-bottom plane was also a Sudoku. ...
2
votes
1answer
152 views

The France Public Holiday's Distance Grid

French Public Holidays We consider the following rules that apply to the 11 French public holidays : New Year's Day : 1st of January Easter Monday : Monday following Easter Sunday which is the next ...
1
vote
0answers
80 views

TestGameExamination [duplicate]

You are given 10 sets of papers with 10 questions each. Answer to each question is from 1 to 4. You somehow get your hands on the answer sheets and able to memorize each answer (Answer sheets only ...
10
votes
2answers
1k views

How many bishops to walk across the board?

N bishops are placed on a standard 8x8 chess board. Each bishop can move normally but after touching or moving over an square, that square is considered marked. A bishop cannot pass over or land on ...
7
votes
3answers
180 views

Placing The Black King

In this position, White’s sole aim is to castle. But in order to do so, they must promote their pawn to a queen to force a Black bishop move. The 10 black kings represent where Black’s king can safely ...
7
votes
4answers
362 views

No Square Allowed

On a Chessboard, place as many chess pieces as you can. Position the center of each piece on the center of a square. Avoid placing any 4 pieces at the corners of a square (even a tilted square). ...
7
votes
1answer
156 views

What is the minimum-value piece combination necessary to checkmate in this game of Crazyhouse?

Imagine you're playing a game of crazyhouse, which operates like standard chess, except that you have a pocket of captured pieces that you can drop on the board in any legal location as your move. ...
4
votes
1answer
103 views

Maximum number of legal moves after n moves in a chess game [closed]

Given the chess start position : What is the maximum number of legal moves white can play after $n$ full moves? We will assume black is helping white in this task. I want the best answer you could ...
2
votes
1answer
195 views

The Big Cube and Squares Puzzle

The following logical puzzle is mainly inspired by a mathematical contest I went to. Part A You are given a cube. How many planes cross this cube by at least 3 vertices? This number will be named $...
7
votes
3answers
436 views

What is the minimum count of steps required to complete this maze correctly?

Here's a map: How to play Legend: B = Boost X = Objective (•) = Start point Mission: ...
1
vote
1answer
66 views

k-threats Chinese Cannons Chess: Part 2

Inspired from the N-Queens problem, I here propose you a puzzle from Xiangqi wich is Chinese Chess equivalent, mostly played in Asia. The most different piece from Xiangqi is the cannon. You can ...
10
votes
3answers
541 views

Pieces of paper without consecutivity condition

TL;DR: like this puzzle but with an arbitrary number of papers and without the condition that the papers chosen must be consecutive. You are given $n$ pieces of paper, and you write down $n$ distinct ...
4
votes
1answer
77 views

k-threats Chinese Cannons Chess: Part 1

Inspired from the N-Queens problem, I here propose you a puzzle from Xiangqi wich is Chinese Chess equivalent, mostly played in Asia. The most different piece from Xiangqi is the cannon. You can ...
7
votes
4answers
323 views

3 Colors of Chess Pieces Attacking Each Other Once Each

Yes, it's another "Chess Pieces Attacking Each Other" puzzle. This time we have 3 colors. Your goal is to place as many of the same type of chess piece (excluding pawns since you can't define the "...
6
votes
1answer
94 views

Freedom of many choices

There are 40 possible move options for both White and Black players in the starting position. The 4 knights and 16 pawns all have 2 options. If all the pieces are still on the chessboard, how would ...
6
votes
1answer
134 views

Most moves by Most number of Pieces

Using one color, White or Black, place as many chess pieces (kings, queens, bishops, knights, rooks, and pawns, or combinations thereof) as you can on a checkerboard so that when the number of pieces ...
2
votes
1answer
97 views

Footmen And Friends #3: Eviction

Welcome to Episode 3, where we have a strange puzzle for today. Pawns aren't legally allowed on the first and eighth ranks, but today we make an exception for the sake of creating another long but fun ...
3
votes
1answer
80 views

Electrical Roughing-ins

The 27 junction boxes at the ends of electrical conduits must all have a green and red wire taps for the lighting fixtures. Only one wire fits the conduits for safety. The wires should be connected on ...
3
votes
3answers
205 views

Does there exist a way to find the least number of trials when a certain weight is requested?

I'm not very sure how to tackle this sort of problem: It is as follows: At a groceries store there is a two pan scale and two weighs which are of $250\,g$ and the other of $500\,g$. It is known ...
0
votes
2answers
92 views

How can I find the total number of rabbits if they reproduce at a constant rate? [closed]

The problem is as follows: Roger adopts two female rabbits and two male rabbits. Three months later each female rabbit gives birth three female rabbits and three male rabbits. Assuming that if ...
5
votes
1answer
170 views

Footmen And Friends #1: A Long Ways Away

Tonight premiers the first show of Footmen And Friends, a show dedicated exclusively to kings and pawns. Let's give these soul-men of chess a chance to shine instead of their big sisters and brothers! ...
7
votes
1answer
109 views

What is the minimum-sized Blokus board which can contain all pieces?

Rules: Each player has the twelve pentominoes, five tetrominoes, two trominoes, one domino, and lone square. These may be flipped and rotated in any manner. The board on which these are to be placed ...
12
votes
3answers
1k views

How many chess pieces do we have to put at least?

In a $8\times8$ chessboard, a cell is qualified if an adjacent cell (a cell which is on top, left, below, or right of the cell) excluding itself has a chess piece on it. How many chess pieces do we ...
12
votes
3answers
383 views

Fewest polyominoes to construct digits

What is the fewest polyominoes you need so that any one of the numbers $0$ to $9$ can be constructed? When constructing, polyominoes may be rotated and flipped, but may not overlap. Bonus: How few ...

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