# Questions tagged [optimization]

A puzzle where you have to optimize a certain objective function (maximize profit, minimize cost). There should ideally be a provable best answer, to avoid making the puzzle into an [open-ended] game.

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### Make the three products equal and as large as possible

Beginner puzzle This puzzle is intended to be suitable for people who are new to puzzle solving. Clarification: Both experienced solvers and new solvers are welcome to post solutions to this puzzle. ...
745 views

### Make a square table top with the minimal needed amount of straight cuts

inspired by : Make a square table top with six (or fewer) pieces A carpenter has three pieces of beautiful wood, measuring 12 inches, 15 inches, and 16 inches square, respectively. They want to use ...
444 views

### Make a square table top with six (or fewer) pieces

A man had three pieces of beautiful wood, measuring 12 inches, 15 inches, and 16 inches square respectively. He wanted to cut these into the fewest pieces possible that would fit together and form a ...
227 views

### Dishonest dungeon staff

You are faced with the difficult task to set up a dungeon for adventurers. However you made a deal with the guild: any adventurer brave enough to beat the dungeon and reach the treasure room will be ...
635 views

### Circles crossing every cell of an NxN grid

What is the least number of circles you need to draw, such that every cell of an NxN grid is crossed? A circle crosses a grid cell if one of the points on its circumference lies completely inside the ...
7k views

### How many Chess Pieces are needed to control every square on the board? No Piece Restriction

You may use as many pieces as you like. Pieces do not control the square they occupy. Accepted Answer goes to the person that has the least score. Piece cost: Pawn - 1 Knight - 3 Bishop - 3 Rook - ...
5k views

### How many Chess Pieces are needed to control every square on the board?

You may only use pieces in the original set, and all your pieces must be the same color. The king is not allowed. Pawns do not get promoted. Pieces do not control the square they occupy. Accepted ...
1k views

### Winning chance in coins game with fixing

A player plays the following solitaire game. The game consists of as many rounds as are needed to produce a result. They have 20 fair coins, which may in any round be live or fixed; each coin starts ...
2k views

### Circles crossing every cell of an 8x8 grid

What is the least number of circles you need to draw, such that every cell of an 8x8 grid is crossed? A circle crosses a grid cell if one of the points on its circumference lies completely inside the ...
293 views

### Number operation problem - find minimum number of operations

On the blackboard, there are nine numbers from 1 to 9. In each operation, two of the numbers are chosen, erased, and replaced with their sum and difference. If two identical numbers appear on the ...
864 views

### Flip counters in a grid so that they alternate in color

Beginner puzzle This puzzle is intended to be suitable for people who are new to puzzle solving. Clarification: Both experienced solvers and new solvers are welcome to post solutions to this puzzle. ...
712 views

### Connecting 3 circular power timers to lights so that they turn for one day on Christmas

My friend gave a question to me. I am not sure if it is an original puzzle, but he has 2 lines of Christmas lights and 3 circular timers with 96 switches apiece. Each switch turns on power for 15 ...
3k views

### Two prisoners and twenty marbles

Two prisoners are planning their escape. Their cells are locked with a padlock that must be opened with a 5-digit code (numbers 00000 to 99999). Each prisoner knows the code of the other prisoner's ...
448 views

### Tile a square as small as possible using two different sizes of square tiles

There are two types of square tiles. One type has a side length of 1 cm and the other has a side length of 2 cm. What is the smallest square that can be made with equal numbers of each type of tile? ...
437 views

### 75 integers are squared or cubed: minimum distinct results? [closed]

75 different integer numbers are written on a blackboard. Each is erased and replaced with either its square or its cube, the operation being random for each. What is the minimum quantity of different ...
2k views

### 6 Water Glasses Upside Down

There are 6 water glasses as shown in the picture below: You need to turn all of them upside down with the rules below: You have to choose any 5 of them at every turn. Chosen ones need to be turned ...
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 ...
1k views

### Minimum number of questions for real treasure

There are 2000 treasures, among which only one is real and the others are fake. There are also 2000 knights, among whom one always tells the truth while the others always lie. You can ask the knights ...
179 views

### Approximate ln(2) out of small numbers

Given numbers 1,2,...n, the goal of this puzzle is to make a number as close to the mathematical constant $\ln(2) ≈ 0.69314718055$ as possible. Rules You can only use the four mathematical ...
2k views

### Fewest number of prisoners needed

You are an assistant to the king, who has scheduled a party tomorrow. There are 1000 wine bottles in the king's possession, and unfortunately, 3 of them are poisonous. Consuming from any of these ...
1k views

### Hexominos from pentominos, heptominos from hexominos

All twelve pentominoes can be obtained by attaching a single unit square (edge to edge) to one of the squares that make up one (or more) of the following four tetrominoes: a) What is the least number ...
461 views

### cheapskate jigsaw inc

Jigsaw puzzles are awesome and making them is an easy way to get rich. So I bought a cutting machine to make puzzles. Unfortunately I could only afford the cheapest machine available. All pieces are ...
2k views

### General attacking chessboard squares

This is a general version of this beautiful puzzle. Place any number of standard chess pieces on a 8x8 chessboard, such that there is at least 1 empty square attacked by exactly 1 piece, at least 1 ...
600 views

### New record for minimally clued 5x5 Hidato

CrSb0001 has been studying the minimum number of clues to force a unique solution in Hidato for variously sized boards. They came up with a 5x5 Hidato with 5 clues but it was found that it has ...
1k views

### What is the minimum amount of numbers needed to create a 4x4 Hidato with a unique solution?

Goal of Hidato: Fill in a grid with a series of consecutive numbers that connect each other horizontally, vertically, or diagonally. So I have been working on figuring out the minimum number of ...
1 vote
192 views