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.

Filter by
Sorted by
Tagged with
37
votes
11answers
4k views

Sudoku net that is always solvable

A sudoku net is a 9x9 grid where every cell is either (blank) or has a cross (block). A random solved sudoku is chosen. The net is placed on top of the sudoku (in any of the 4 ways). We can only see ...
3
votes
1answer
615 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 ...
5
votes
4answers
661 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,...
9
votes
3answers
3k views

$n$ couples crossing a river

There are $n$ couples on one side of the river. Nobody is on the other side. They have a boat that accommodates up to 2 people. For every trip across, someone(s) must bring the boat back as well. The ...
5
votes
3answers
440 views

$n$ monsters and $n$ people

There are $n$ monsters (M) and $n$ people (P) on the left side of a river. Nobody is on the right. They have a boat that can hold up to 2 beings. At no point on time may either of these be true: $$M_{...
2
votes
8answers
218 views

Pass the Baton competition 6 members teams

The following diagram depicts a Pass the Baton tournament (Note: due to a merge, some of the answers below use this image instead.) Each team consists of 6 members, 2 at the central point $E$, and ...
7
votes
3answers
935 views

Can you create a Minesweeper puzzle with 'information crossover'?

The object of this puzzle is to construct a Minesweeper grid with a special property. The grid can be any shape, but it must have four labeled squares around the outer edge. Like this: The four ...
9
votes
1answer
651 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 ...
11
votes
1answer
558 views

Bouncing Robots: Graphical Puzzle [closed]

Robots are indicated by the arrowhead shapes and the labels "r", "y", "b", "g". The label obviously corresponds to their color. The aim of the puzzle is to pick up the shapes and put them down in the ...
16
votes
8answers
2k views

Rigged casino that prevents pairs

This question is still active as the answer from @Sleafar has just arrived. Not yet solved. Scenario The heads of 3 top terrorist organisations are planning to play an extremely high-stake poker ...
8
votes
5answers
1k views

Turn 16 into 25. You have 4 magic spells. Can you do it?

You have been given the number 16. You also have 4 magic spells. You have to use the spells to turn 16 into 25. Each spell changed your number a specific way, but the objective is never altered, you ...
13
votes
3answers
893 views

Searching for a secret door

You have reached the final stage of a game show, and now face an endless row of doors labelled $\ldots,-3,-2,-1,0,1, 2, 3,\ldots$, going from minus infinity to plus infinity. Your goal is to detect a ...
27
votes
10answers
3k views

One prize, infinitely many choices

Having reached the final stage of a game show, you face an endless row of doors labelled $1$, $2$, $3$, ... The game show host has selected a whole dollar amount, and has put this exact amount as a ...
32
votes
3answers
3k views

Cross-road optimization - what is the proper way to solve this type of puzzle?

This puzzle has 3 levels of increasing complexity. Each "level" is separate and complete, so feel free to post partial solutions to the individual levels only. I'm most interested in the ...
4
votes
1answer
510 views

Tune a podracer and choose the pilots by solving the podracer tuning equation

A long time ago, in a galaxy far, far away... These are troublesome times: The Galactic Republic is gone, the Jedi were exterminated due to Order 66, Vader and Palpatine rule the galaxy with absolute ...
26
votes
2answers
3k views

The tilted labyrinth - Can you find the fastest path in this 3D-puzzle? (Simulator now included.)

This is a puzzle was inspired by the board game labyrinth, which I very much enjoyed as a kid. It either requires very good 3D-visualization skills in your brain or some paper & scissors work. (...
3
votes
4answers
1k views

Sell the fuel and become a Millionaire [duplicate]

You are living in the 22nd century. The fuel prices are unimaginably high and it is very rare to get, so the Government has introduced some new laws to control fuel smuggling. Rule 1: One cannot ...
5
votes
2answers
658 views

What to do when the official Rubik's cube solving sequence breaks?

So, the official guide shows you exactly how to solve the white cross, first layer, etc. but on the second layer, assume you've completed every little square but one (and edge) and that there's 2 ...
10
votes
1answer
1k views

Ernie and the Geometric Ginger Cookies

Ernie loves cooking and it's always worth the wait as he follows his curiously precise recipe to make Ginger Crunch Cookies. So I was happy to drop around when he invited me to help test his latest ...
34
votes
8answers
6k views

Dinosaur egg drop

Archeologists discover two dinosaur eggs, and you are given the chance to test the durability of these eggs (bad move on their part). Suppose that these eggs will absorb a specific amount of force ...
1
vote
2answers
537 views

If The Knights and Knaves got together [closed]

If the island of knights and knaves got together and there were n people, including a joker, how many questions would it take for all of the knights and knaves found the joker? Nobody knows who each ...
11
votes
4answers
1k views

Optimization of area

You have a closed cord of length 100 meters which touches point $P$. There is a line $L$ whose closest point is 20 meters from point $P$. The value of a layout of cord is defined by the area ...
13
votes
2answers
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 ...
6
votes
3answers
443 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 ...
10
votes
2answers
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 ...
4
votes
1answer
359 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: ...
42
votes
7answers
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
votes
5answers
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 ...
11
votes
5answers
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 ...
43
votes
17answers
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 ...
7
votes
1answer
436 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 ...
17
votes
2answers
840 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 ...
1
vote
2answers
400 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 ...
2
votes
3answers
1k 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 ...
4
votes
2answers
657 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 ...
5
votes
2answers
435 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 ...
6
votes
2answers
1k 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"): $$ \...
6
votes
1answer
9k 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 ...
30
votes
5answers
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 ...
18
votes
3answers
3k 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, ...
11
votes
7answers
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 ...
30
votes
3answers
4k 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 ...
79
votes
15answers
88k 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 ...
7
votes
1answer
864 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 ...
14
votes
2answers
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 ...
21
votes
1answer
1k views

Worst case scenario in 2048

The game 2048 can be thought as a two player game, where one player shifts the table around to get to the 2048 tile, while the other player tries to hinder them by putting down 2s and 4s on the table. ...

1
7 8 9 10
11