# 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 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 ...
• 8,601
218 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 ...
• 41
438 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 ...
• 9,876
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 ...
• 8,631
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 ...
• 53
633 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 ...
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 ...
863 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. ...
• 9,876
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? ...
• 9,876
929 views

### 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. ...
• 9,876
433 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 ...
• 595
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 ...
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 ...
• 69
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 ...
• 2,241
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 ...
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 ...
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 ...
• 13.8k
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 ...
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 ...
• 2,241
1 vote
175 views

### How long will it take for the horse to be captured?

Source: https://open.kattis.com/problems/ambush Problem: When Farmer Oskar doesn’t watch his cows closely enough, they tend to wander off into the forest to hunt for horse spies. To catch an enemy ...
• 103
1k views

### An Amazing Configuration

Ed Pegg found in December 2019 this amazing configuration consisting of 22 points in 28 lines of 4. On those points place 22 different positive integers such that the sum of any of the four points in ...
3k views

### Pythagorean pentagons

To follow up on the theme of so called "pythagorean" dissections, here is one more for you to chew on. I hope you don't get bored. The pentagons above have sides respectively 3, 4 and 5. ...
• 29.8k
1 vote