# Questions tagged [optimization]

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

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### Coloring the Chess Board

We have 8x8 Chess board like grid (8x8 2D matrix) and we are trying to color every single square/cell. But the rules are interesting; You may start from any square you want and color that square for ...
655 views

### A tour of 36 cities

Each of 4 people is touring 36 cities separately. Each of the 36 squares in the illustration below represents a city. To make the answers shorter, each city has been given a 1-character name, from A-Z,...
616 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 ...
2k views

### Can you open the door or die?

You wake up and find yourself in a very strange room with a single door. You find a note on the ground surrounded by lots of cards: There are 66 green and 66 blue door cards on the ground. If you ...
594 views

### What is the minimum number of steps to solve this cloning particles on chessboard puzzle?

I'm creating a puzzle based on the idea from this numberphile video: pebbling a chessboard. You can see a working (yet unfinished) version here. I would like to give the user a feedback of how well ...
294 views

### Savage Road Signs (Part 3)

You only need to have read Part 1 to understand this question, reading Part 2 will only help understanding the epic storyline. Your daughter refuses to talk to you even though you have (once more) ...
387 views

### Optimal path around a variable-position wall [closed]

This is a harder version of the fixed wall variation. Every day you walk across a flat plane from a point $A$ to a point $B$. The points are $3$ miles apart. However, every day there is a 50% ...
284 views

### How can 32 teams rotate through 8 games without overlaps? [closed]

So I have to arrange a rotation schedule for a tournament. We're aiming for 32 teams. There will be 8 stations and 4 teams competing simultaneously at each station. We want all 32 teams to hit each ...
3k views

### Smallest PRIME containing the first 11 primes as sub-strings

In Smallest number containing the first 11 primes as sub-strings, @Alconja successfully found the smallest number which contains the first eleven primes (2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31) as ...
3k views

### The grades of the students in a class

You are a new Math 102 professor in a university class of 88 students and would like to learn their grades from previous semester to know your students better and put a note of it to get an idea how ...
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 ...
287 views

### Get 6 pawns in file A or H without promoting

This is wholly inspired by Get 6 pawns in file A or H Is it possible for either white or black to get 6 pawns of the same colour in file A or in file H (you must choose one) without promoting?# If ...
630 views

### Maximize 'chains' in a Sudoku

Yet to be solved. Take 2 numbers such that $N, M \in \{1,2,3,4,5,6,7,8,9\}; N \ne M$. Start with a solved 9x9 Sudoku grid. Find any $N_1 = N$. Find an $M_1 = M$, in the same row as $N_1$. In the ...
195 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. ...
626 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 ...
581 views

### This ant sure is smart. But how fast is it?

A mad scientist uses ethically questionable methods to study the spatial cognition of ants. Last time, he left his lab ant in a cubic room and filled it with painfully intoxicating gas, capable of ...
200 views

### De-zephyr The Solution!

Here's another original chess problem of mine for you all to solve today! In the following position, White wants to stalemate Black even though they can win, for unknown, unclear, unexplained, and ...
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! ...
216 views

### Square Spin #3: Hickory Dickory Dock

Square Spin History: #1>#2>#3 Recap of the Rules Basic rules from #1 Ambiguity, Un and Re squares from #2 Problem #3: Hickory Dickory Dock The mouse ran up the clock. ...but ...
81 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 ...
483 views

### Are there basic weighing puzzles requiring adaptive strategies?

Let us define a basic weighing puzzle as such: There are <number> identical balls, except one weighs <more/less/a different amount than the others> A balance scale may be used to weigh two ...
210 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 ...
264 views

### How many different results?

$a,b,c,d,e,f,g,h,i$ are real numbers and you would like to calculate the equation below by adding as many paranteses as you want: a-b^c-d/e+f/g^h*i What is the maximum amount of different results ...
199 views

### Make the largest box from a cardboard sheet Chapter #2

Please see: Make the largest box from a cardboard sheet Thanks to his older brother's friends: @Oray, @Weather Vane and @mlk, the boy managed to make as large cardboard box as possible. Unfortunately,...