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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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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 ...
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 ...
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 ...
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 ...
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 ...
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 ...
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 ...
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 ...
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 ...
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 ...
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 ...
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 ...
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 ...
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 ...
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 ...
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.
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 ...
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 ...
3answers
266 views

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 ...
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 ...
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 ...
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 ...
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 ...
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 ...
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 ...
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 ...
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 ...
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 ...
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 ...
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 ...
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 $5$...
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. ...
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 ...
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: ...
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(...
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 ...
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 ...
1answer
261 views