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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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5
votes
3answers
1k views

Hacking an electronic keypad v2

This is related to Hacking an electronic keypad. You are a spy trying to break into an enemy facility. The back door is protected by an electronic keypad lock. You know that this particular lock is ...
5
votes
2answers
719 views

How much money can we make? v2

This is follow up question to How much money can we make? My five friends and I used to loan each other money all the time. But over the past several years we have moved apart. We don't trust ...
2
votes
1answer
263 views

The A-B chocolate puzzle!

Imagine you have 2 types of chocolates (A and B). You randomly pick up two chocolates at once from your bag in a specific pattern. If the same type of chocolates come out, you give them both to your ...
23
votes
3answers
984 views

How much money can we make?

My five friends and I used to loan each other money all the time. But over the past several years we have moved apart. We don't trust PayPal, banks, or the postal service so transferring money over ...
1
vote
1answer
269 views

Scheduling Meetings

I came across this problem in real life and thought it could be made into an interesting puzzle. I will enjoy seeing how my eventual solution could be improved! Here's the situation. There ...
9
votes
2answers
517 views

Smallest Army on a chessboard

This is actually similar question to Biggest army on a chessboard. But it is kinda different way of asking. In this game, you are supposed to put the least amount of pieces into the board where there ...
8
votes
3answers
558 views

Acids and Bases

I have 6 solutions. 3 of them are acids, and 3 of them are bases. The acids and the bases (HCl and NaOH respectively) both have solution with a concentration of $0.1M$, $1M$, and $10M$. I don't know ...
30
votes
5answers
3k views

Biggest army on a chessboard

Reminder: Everybody knows that we can place 8 queens in a chessboard without threatening each other (see here). Same reasoning can be applied for knights, bishops, rooks and kings. Giving ...
-4
votes
1answer
150 views

Maximize gold bars [duplicate]

You have encountered 100 gold bars in a cave. In the cave, a goblin shows you 3 holes in the wall. He says one hole will triple what you put in it, one hole will leave it as the same amount, and one ...
8
votes
1answer
2k views

99 chips into more chips

You are at a casino in Vegas and you have earned 99 chips by playing poker! While you are checking out a slot machine, someone comes to you and congratulates you that you have a chance to make more ...
7
votes
2answers
432 views

99 chips into more chips V2

This is follow up question of 99 chips into more chips, which is originally: You are at a casino in Vegas and you have earned 99 chips by playing poker! While you are checking out a slot ...
16
votes
7answers
2k views

Soldiers in the Parade Ground

Twenty-five soldiers are standing in a parade ground consisting of a five-by-five grid of large concrete slabs, laid out in a neat north-to-south, east-to-west square array. Each soldier is standing ...
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 ...
6
votes
3answers
380 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 ...
17
votes
2answers
911 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 ...
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
490 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
179 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
973 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 ...
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 ...
4
votes
2answers
573 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 ...
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 ...
9
votes
1answer
259 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 ...
6
votes
4answers
668 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
768 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 ...
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
275 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 ...
3
votes
1answer
425 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 ...
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 $5$...
5
votes
4answers
489 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
413 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: ...
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
307 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
3answers
829 views

16 Two Colored Line up v2

This is the follow-up question for 16 Two Colored Line Up This time, you are not supposed to solve it, but find the worst possible arrangement for each square, which will make the number of steps ...
11
votes
2answers
760 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
441 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
844 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
462 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
319 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 ...