# 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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### How many clues are sufficient to solve an X-Sudoku puzzle?

I've heard that for standard Sudoku a minimum of 17 clues are needed to solve a puzzle, but I imagine it might be slightly less in the variant X-Sudoku, because I assume there would be slightly fewer ...
464 views

### Overlap two Chess Games

Create two valid Chess games (A and B) with the minimum number of moves (you will sum the number of moves of A and B) such that overlapping the two games creates a valid chess position. The following ...
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986 views

### Flashlight and 6 batteries

In front of you are 6 batteries and a flashlight. You know that 4 out of the 6 batteries are fully charged, and 2 out of the 6 batteries are empty, but you don't know which ones are charged and which ...
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### Placing dominoes on a 16 × 14 grid

I am placing dominoes on a 16 × 14 grid. Dominoes must be either horizontally or vertically. Each domino must cover 2 small squares. What is the minimum number of dominoes that can be placed so that ...
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### When Beatrix stops placing dominoes on a 5x5 board, what is the largest possible number of squares that may still be uncovered?

Beatrix places dominoes on a 5x5 board, either horizontally or vertically, so that each domino covers two small squares. She stops when she cannot place another domino, as in the example shown in the ...
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334 views

### Combine 8x8 square grid and 15x15 square grid into 17x17 square

You have an $8\times8$ square grid and a $15\times15$ square grid. You want to dissect them and combine them into a $17\times17$ square. What is the minimum number of pieces required? Only cuts along ...
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152 views

### Weigh 15 boxes with a digital scale, but you can’t understand the number system

This puzzle is inspired by the puzzle 14 coins problem but you can't understand the scale. In this weighing puzzle, you have 15 boxes, each one weighing 1, 2, 3, and so on until 15 arbitrary units....
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822 views

### Solid border Yin-Yang

Yin-Yang is a grid deduction puzzle with the following rules: Fill each cell with either a black circle or a white circle. All circles of a given color must form a single orthogonally-connected ...
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375 views

### Superman looking for Supergirl

Superman needs to find Supergirl in a hotel room. Unfortunately, the hotel is also "super" and has 100,000 rooms arranged in a row. Each room has a door to the corridor and to the adjoining ...
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259 views

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### Tiling a 16x16 square with 1x4 rectangles

Consider a 16x16 square subdivided by grid lines into unit squares. It is easy to completely tile (no overlaps, no gaps) this square with 64 1x4 rectangles. Each 1x4 rectangle in the tiling (no ...
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192 views

### The ultimate backgammon

The following position, where one player has borne off all their checkers while all of the other player's checkers are on the bar (thus losing a backgammon), is reachable by a legal sequence of dice ...
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### 11x13 Chocolate Banana Followup

Your goal is to maximize the absolute difference of the numbers marked ?. (? marks indicate region areas. They may or may not ...
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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 ...
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416 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 ...
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512 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 ...
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### 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 ...
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324 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
698 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 ...
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### 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 ...
• 36.5k
906 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. ...
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484 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? ...
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1k 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. ...
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489 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 ...
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### 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 ...
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### 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
419 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 ...
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