# 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.

828 questions
Filter by
Sorted by
Tagged with
7k views

### Connect four towers by roads

Four guard towers are situated in a square formation of side length 1km. A general wants to build roads to connect the towers so that one can walk from any tower to any tower along the roads, possibly ...
• 26.8k
464 views

### Abalone Migration

Abalone is a 2-player board game. Here's a brief explanation from Wikipedia: The board consists of 61 circular spaces arranged in a hexagon, five on a side. Each player has 14 marbles that rest in ...
• 5,756
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 ...
• 9,102
418 views

### Equal Chess Control

Is it possible to setup a chess board where every square on the board is only controlled once. Occupying a square does not mean controlling it. If it is possible, with how little pieces? Piece Cost: ...
• 14.5k
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 - ...
• 14.5k
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 ...
• 14.5k
538 views

### How many Queens on a board

Similarly to this question: How many Queens to threaten themselves. What it the maximum number of queens you can place on an 8*8 board such that each queen is attacked precisely twice: with no other ...
• 12.9k
2k views

### Sorting cards using max 3 stacks

You have a stack of N cards numbered from 1 to N in random order. You want to sort the cards in ascending order using the following procedure: Your initial stack is stack 1. You distribute the cards ...
• 29.8k
2k views

### How Many Queens to Threaten Themselves?

How many queens can be placed in a standard $8*8$ chessboard to threaten each of them exactly once by other queens?
• 5,756
9k views

### A blanket for my baby snake

Mama snake wants to knit a blanket for little baby snake. She is not a dissipater and wants to make the blanket of a minimal size (area). But her baby snake is quite a lively baby and it always ...
• 731
456 views

### Shortest time interval measurable via burning a rope

You are given some matches, a rope, and a pair of scissors. The rope burns irregularly and takes 60 minutes to burn end to end; however, we know that the burn rate at distance $x$ from the left end is ...
• 804
912 views

### Santa Claus flies to the South Pole

It is a little known fact that Santa Claus is in fact a vampire. Why else would he spend so much time near the North Pole and travel only at night? Yes, he fears daylight! His problem is that ...
• 29.8k
6k views

### Divide 3 cakes into 4 equal parts?

You have three cakes of diameter 20cm, 16cm and 12cm respectively as shown in the figure. They all have the same height. Now your task is to divide these 3 cakes into 4 equal parts and you are ...
• 1,313
1 vote
422 views

### Bottle rinsing with fixed amount of wash water

Given $L$ units of wash water, we want to wash out a vessel (eg, a milk bottle, honey jar, chemistry flask...) using a series of rinses that minimize the amount of Stuff other than water remaining in ...
2k views

### Folding a hexagon to a rectangle or square, with uniform overlap

A piece of fabric shaped like a regular hexagon with unit-length sides is given, with vertices A...F and center O. Let a fold correspond to folding some fabric along a straight line, without ...
808 views

### What's the largest number that can be obtained in the process of solving a numbers game on Countdown?

Countdown is a British game show in which people try and make the longest possible word out of nine given letters, reach a target number using six given numbers and basic arithmetic, and then solve a ...
486 views

### Land claim staking

It was traditional during the times of the Oregon Trail and the gold rush that men founding new towns were allowed to stake their claim on land upon arriving to the west coast. Suppose a man is ...
• 2,116
2k views

### What is the smallest tic-tac-toe board to have a winning strategy?

There is not winning strategy for 9cell 3x3 board. There is a winning strategy for 16cell 4x4 board, or even for 10cell "3x3 + 1_cell_near_a_corner" board (see M.Gardner "Mathematical games"):  \...
• 16.2k
12k views

### Maximal number of steps needed to solve 2x2x2 Rubik's Cube

What is the maximal number of steps that a computer (using the fastest algorithm) would need to solve an arbitrary 2x2x2 Rubik's Cube configuration? Are there any other known algorithms that will ...
• 16.2k
6k views

### Two spies throwing stones into a river

There is a puzzle about two spies: Two spies must pass each other two secret numbers (one number per spy), unnoticed by their enemies. They have agreed on a method for doing this using only 26 ...
• 16.2k
4k views

### Knights and jokers

There are $N$ men. $K$ of them are knights, $M$ of them are jokers. $N$ is known, $K$ and $M$ are unknown. You know that: $K + M = N$, $K \gt M$, $M \ge 1$, $N$ is odd. Knights always tell the truth, ...
• 16.2k
2k views

### Is there a move-efficient way to rotate the center pieces on the Octo-Star?

I'm looking for a more efficient algorithm to rotate the center column of the Octo-Star puzzle 45 degrees. The situation below occurs when four properly-oriented edges are next to each other, ...
3k views

### Fastest way to collect an arbitrary army

I am looking for solution of this puzzle: There is a kingdom with a square shape with sides of length 1. The castle is located at the center of the square. At the castle the king lives under the ...
• 16.2k
5k views

### How many squares can 4 queens control?

Though there is no strict mathematical proof, it has been shown via brute-force that no arrangement of 4 or fewer queens can control every square on a standard 8x8 chessboard. So, out of the 64 ...
• 471
208k 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 ...
938 views

### What is the fewest number of clues on a rotationally symmetrical sudoku grid with a unique solution?

It is known that the minimum number of clues a sudoku must have to have a unique solution is 17. But on every website I've seen for them, I haven't found any that are rotationally symmetrical. I once ...
2k views

### How many clues are required to ensure Einstein's Puzzle is solvable?

I used to play Einstein's puzzles a lot when I was younger, and very quickly learned to assess quite rapidly whether I thought a puzzle would be a quick solve or more time-consuming, but I never ...
• 333