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Questions tagged [optimization]

A mathematical puzzle where you have to optimize a certain objective function (maximize profit, minimize cost).

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17
votes
2answers
918 views

numbers want to cross a river, but their sum must be a square number

In the world of numbers, numbers 1 to 9 want to cross a river, They have a boat which can take 1 to 3 numbers, But sum of the numbers must be a square number. The boat can not sail back itself, so ...
6
votes
3answers
381 views

The Alchemist's brew

I'm an Alchemist and I want to prepare Universal Panacea. That's a precious thing and I will be able to sell it for good money. The complete recipe for the Panacea is of course very complex (and ...
40
votes
7answers
5k views

Amnesiac in a ring shaped palace

Related: Turn off all lights in a ring-shaped palace Your boss has trapped you inside a ring-shaped palace, and all you know about the palace is that there are some number* of identical rooms, each ...
10
votes
1answer
352 views

Minimize the intersection area

You are given two identical pieces of paper of size $a \times \sqrt{2} a$, like the standard DIN A4 paper. Put one paper on top of the other, such that none of the corners is under or above the other ...
1
vote
1answer
278 views

The counterfeit coin [duplicate]

You have 9 coins. One of the nine is counterfeit. The counterfeit coin can be distinguished by weight - it is heavier than the rest. Using a balance scale only twice, find the counterfeit coin.
13
votes
1answer
495 views

Hiding Cat Puzzle on a Grid

The Youtube channel MindYourDecisions posted a video about the "Hiding Cat Puzzle". In the puzzle, you have a line of five boxes, one of which contains a cat. You don't know where the cat is, and your ...
-1
votes
2answers
178 views

Best strategy to finding gas station [closed]

We need to refuel and we don't know where the nearest gas station is. We are at a crossing which looks like: ← ↑ →. What is the best strategy to find the gas ...
5
votes
3answers
266 views

A Counterfeit $100 Bill among 93 Bills

You have $93$ of $100 bills and there is a counterfeit 100 dollar among them. You do not know which one is counterfeit bill. You go to the bank and ask whether if there is counterfeit among a group of ...
2
votes
1answer
181 views

How many drops you need to make. You are allowed to break 2 eggs in the process [duplicate]

You are given 2 eggs. You have access to a 100-story building. Eggs can be very hard or very fragile meaning it may break if dropped from the first floor or may not even break if dropped from 100th ...
9
votes
2answers
710 views

Warehouse Maximum Capacity

You own a warehouse which is a 7x7 grid of cells. You must arrange a maximal number of boxes in the warehouse so that you are able to travel to any given cell. Here are the specific conditions: You ...
2
votes
1answer
997 views

3 cannibals and 3 missionaries on different side of the river

Three missionaries on the left side of a river and three cannibals on the right side of the river want to cross a river using a boat which can carry at most two people, The boat is on the cannibals ...
10
votes
1answer
264 views

Get 6 pawns in file A or H without promoting

This is wholly inspired by Get 6 pawns in file A or H Is it possible for either white or black to get 6 pawns of the same colour in file A or in file H (you must choose one) without promoting?# If ...
12
votes
4answers
1k views

Get 6 pawns in file A or H

This is somehow inspired by my other chess related question: Possible pawn combinations How can you get 6 pawns (white or black) on a chessboard on the files A or H using legal moves? Start with a ...
6
votes
4answers
669 views

Radar towers in a military field

The military field has rectangle shape with the dimension of 16 km to 12 km and recently there are some drone activities around the area and drones are not welcome to the military region! Your ...
12
votes
5answers
772 views

More than equilibrium

Assume you have 2 identical metal cubes, the only difference being their temperatures $T_1 = 0 \, \text{°C}$, $T_2 = 100 \, \text{°C}$: The task is now to transfer as much heat as possible to the ...
3
votes
1answer
276 views

30 Soda with 30 Crown Cork

You want to buy some soda, and there is a special offer saying that if you bring $7$ crown corks of soda, they will give you an extra soda! You notice that you have enough money to buy at most $30$ of ...
11
votes
1answer
1k views

Futoshiki Puzzle with the least amount of clue

You are supposed to create a new $5$x$5$ Futoshiki puzzle with the least amount of clues possible, but this puzzle needs a unique answer. In other words, What is the minimum number of clues for $5$...
26
votes
6answers
5k views

A Special Parking Lot

There is a special kind of parking lot that stores special 1x1 cars that only can move to adjacent squares not including diagonals if they are empty (provided no car occupies the square). Every car ...
3
votes
1answer
427 views

Three baskets with numbered balls

Three baskets and some balls are given to you. You are supposed to put these balls into these baskets by writing some positive numbers on the balls. But: The numbers you are supposed to write on them ...
5
votes
4answers
490 views

Time traveler treasure Hunt

A time traveler is collecting treasures. He is using a space-time ship to transport between 5 different place-rooms. Each place has 1 precious treasure from the ancient times in each of 5 time zones. ...
3
votes
1answer
414 views

8 Train Stations

You are going to build $8$ train stations and the railroads with it in an area. But you are asked to build these stations and their railroads in a very efficient way where there has to be the least ...
8
votes
1answer
513 views

Picking A Number Game

Alice and Bob play a game starting from Alice where Alice and Bob are supposed to write a number to the board, Then the game goes through several rounds between Alice and Bob with the rules below: ...
6
votes
2answers
670 views

Crystal Maze totem pole puzzle

The UK game show "The Crystal Maze" features a puzzle based around a totem pole. The contestant has four different coloured blocks which can be stacked up to make a totem pole. The blocks may be ...
8
votes
1answer
347 views

Megan visits all the stations

The other day I was waiting for a train and had just popped into the nearby branch of Costa Bean for a coffee, when who should I run into but my old friend Megan and her partner Ricky, studying a ...
5
votes
3answers
2k views

Guessing a number game with a twist

Most of us have come across the problem in which a player chooses a number within a range $1-n$ and we have to guess that number by asking minimum no. of questions. That can be done by binary search(...
2
votes
1answer
134 views

How many moves are at least needed to change the order of cubes to a arbitrary order? [closed]

We have several cubes that are ordered as in the picture below: What is the smallest number of moves with which we are able to reach every possible order? Only the order of the cubes in the ...
6
votes
1answer
461 views

How many multiplications to find n^k given n, for general k?

I was looking at the nice puzzle Find $n^{23}$ with the least multiplication. My first instinct for this would have been to find $n^{2^i}$ for each $i$ first and then multiply these together as ...
4
votes
1answer
261 views

Find the maximum number of all-one rows

We've got an $N \times M$ matrix whose elements are either zero or one. For example: $\begin{bmatrix} 1 & 0 & 1 & 1 & 1\\ 1 & 1 & 1 & 0 & 1\\ 1 & 1 &...
5
votes
1answer
314 views

Removing matchsticks to remove all squares

By using $60$ matchsticks, $5\times5$ matchstick matrix is formed as below: There are totally $55$ squares including all type of squares (such as $25$ $1\times1$ squares, $16$ $2\times2$ squares etc.)...
11
votes
2answers
761 views

Mike's Coin Duplicator

This is my first mathematical puzzle on the site. To be honest, I don't know if this should go to M.SE or here. Any grammatical or backstory edits are welcome, as I realized that my English is not ...
3
votes
4answers
442 views

Square Room Tiles

The square floor of a square room was covered with colored 1 square unit tiles.The covering tiles were designed to have different (solid) colored tiles that forms rectangular areas but none of these ...
1
vote
1answer
874 views

The swap puzzle

The swap puzzle Place small coins heads up on the squares marked H and tails up on the squares marked T. Swap the positions of the Heads for the Tails in as few moves as possible. There are two ways ...
6
votes
4answers
433 views

Constructing 0.35 Unit Length

The Problem The medieval equivalent of Bob the Builder has a new job offer: He is to build a box with the measures of $0.35$ units by $0.35$ units by $0.35$ units for a king. There is a little ...
3
votes
1answer
98 views

The Hymns of the Lord - How Many Slates?

From Dante's Infernal Puzzle Collection: Excessive thrift, I learned, may be a sin, when love of wealth does triumph over all, and man forgets his duties to his Lord. In that dark place a preacher ...
10
votes
2answers
473 views

Turn on all squares

Take a square grid of size $a\times b$, with all squares being off. You can tap a square, to reverse the state of that square and all squares located in the same column and row as the tapped square. ...
6
votes
1answer
310 views

Maximize all weights

This question is related to What's the fewest weights you need to balance any weight from 1 to 40 pounds? You had 4 weights to balance any weight from $1$ to $40$ pounds which is answered previously ...
3
votes
2answers
321 views

Return to the Minotaur's Labyrinth

This is an extension of the puzzle The Minotaur's Labyrinth which is inspired by the comments from histocrat. You are trapped (again) in a chamber at the center of the minotaur's labyrinth. There are ...
5
votes
1answer
188 views

Cover 3*2.6 rectangle with the least number convex polygons cut from sheets of given size 1.2*2.4

I want to cover a rectangle of given dimensions ($3\times2.6$) with a minimal number of convex polygons cut from rectangular sheets of material of given size ($1.2\times2.4$). These polygons don't ...
2
votes
2answers
262 views

How many different results?

$a,b,c,d,e,f,g,h,i$ are real numbers and you would like to calculate the equation below by adding as many paranteses as you want: a-b^c-d/e+f/g^h*i What is the maximum amount of different results ...
2
votes
1answer
169 views

King of Captures

The player's black King (above) is about to capture the remaining opponent pieces as continuation of his move and 10 white pieces have already been captured on the same turn/move. What is the position ...
6
votes
3answers
3k views

Impossible 100 Balls Game

You are trying to make an impossible game where there are $100$ balls numbered from $1$ to $100$ and ordered in the worst case and put next to each other. The player is supposed to order the balls ...
28
votes
3answers
3k views

12 Birds in the petshop

You decided to buy 2 birds from a pet shop and went to a pet shop for it. There are 12 budgerigars at the pet shop and you want a male and a female for your home. You cannot distinguish the gender of ...
2
votes
1answer
473 views

Algorithm to Solve Puzzle - Advice Needed

Given the following letters arranged in a circular pattern. A B E C D Each letter can merge with any of its opposite letters to form an adjacent ...
0
votes
1answer
1k views

Packing circles in a rectangle [closed]

You have a rectangle of dimensions $l \times b$ where $l\geq b \geq 1$ and $l,b \in \mathbb R$. How many circles of diameter one unit can be fitted inside this rectangle without overlapping? (Touching ...
7
votes
3answers
806 views

Dinosaur Egg Drop v2

This question is a little different and kinda follow-up version of Dinosaur Egg Drop 1- You have 100 story building and 6 Apatosaurus dinosaur eggs. 2- You have 81 story building and 3 ...
2
votes
1answer
135 views

How to improve “Universal dissection”?

Yesterday I've posted quite easy puzzle: Universal dissection. Now the actual problem. When we deal with 8x8 board with 1 missing cell it doesn't matter whether we allow to flip parts or not, ...
16
votes
4answers
943 views

Universal dissection

Alice has a squared paper 8 by 8. She cuts out one 1x1 square from it, at row N, column M. Bob cuts the rest of the paper into pieces. Once he is done, Alice asks Bob to put the pieces together in a ...
-5
votes
3answers
192 views

How can one reliably prevent pedestrian access to a parking garage, but allow vehicular access? [closed]

Consider a typical private parking garage for a condominium or apartment building. There is currently a typical garage gate that opens and closes (slowly) to allow vehicles to pass safely through the ...
11
votes
6answers
10k views

1 Fake Coin among N Amount of coins

You are given $N$ coins which consists of only $1$ fake coin. You also have a sensitive old-fashioned Pan Balance Scale. You are asked to find the fake coin in totally 5 times weighing on the Pan ...
18
votes
8answers
2k views

30 fake coins out of 99 coins

You are given 99 coins which consists of 30 fake ones. You also have a digital balance scale with perfect precision that shows how much difference between weighs you put on. For example, if you put 10 ...