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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
269 views

land of light bulbs

Leuks is the land of light bulbs, where the bulbs are leading a peaceful life, with no humans at all. Presently there are 100 residents . (Of course, they all are light bulbs!). Let $a_{1}, a_{2}, . ....
5
votes
3answers
198 views

Rawrdon Mamsay pays a visit

Now, I should warn you, this is one of my practical problems; meaning I don't know the solution and the answer's probably anticlimactic (like this or that). Still... My old pal Rawrdon Mamsay is soon ...
11
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3answers
2k views

Find number 8 with the least number of tries

You and your friend plays a game. In this game, there are numbers written on the cards from 1 to 12 on one side (so 12 cards in total). The other side is blank. You can write anything on the blank ...
2
votes
1answer
104 views

In and out, and back in again

With White to move, how long will it take for both sides to cooperate, i.e. this is a helpmate, and checkmate Black? This is based on a problem made made by Otto Blathy. And yes, I know that the ...
4
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1answer
152 views

Find the least expense?

You want to build a shop between three roads in the shape of an equilateral triangle. What would be the best location for the shop so that you can reach each road with the minimum transportation ...
17
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4answers
3k views

Smallest PRIME containing the first 11 primes as sub-strings

In Smallest number containing the first 11 primes as sub-strings, @Alconja successfully found the smallest number which contains the first eleven primes (2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31) as ...
6
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5answers
191 views

Chess Construction Challenge #3-The Inverse Babson

Another day, another task! Today's challenge is to construct four positions, with White to move and win, such that: In each position, White's move is to promote to a particular piece, for a position ...
7
votes
5answers
2k views

Minimum number of lines to draw 111 squares

Find the minimum number of lines to draw 111 squares. For example, you can draw a single square using 4 lines i.e 2 vertical and 2 horizontal. Similar, you can draw a 2 square in the grid using 5 ...
0
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0answers
87 views

Tales of Two Cities (With no Gas Stations in between) [duplicate]

Two cities A and B are 100 miles apart. A person has to travel from one city to the other in his old old car, which can travel only 50 miles with its tank full. Unfortunately, there are no gas ...
11
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2answers
2k views

The economy of trapping

A queen on the center of the board has 27 possible moves. Sometimes a queen can be trapped, like in the position below. Note: This is just an example of a what a trap should be like-every possible ...
6
votes
1answer
952 views

Dodgy Dies: The Puzzling Premiere

Inspired by the "Treasure Hunter Monolith" minigame from Danganronpa V3 Dodgy Dies Guide Terminology Block - a single die on the grid. Cycle - a list of blocks Value - the ...
6
votes
1answer
228 views

Don't bully your cousin at Reversi

Title (only) inspired by Don't bully your little sister at chess Prologue Well, this happened when I played Reversi with my cousin a few days ago... I, not being as nice as @Arnold ...
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2answers
813 views

Flood on the top floor

There has been a water incident on the top floor of a building, and one apartment has suffered some water damage. As in, a lot of water damage. The entire apartment is filled waist deep with ...
7
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2answers
524 views

Don't bully your little sister at chess

This puzzle was inspired by @RewanDemontay's puzzle De-zephyr The Solution!. Rewan kindly granted me permission for making this puzzle and citing his as my source of inspiration. I thought of naming ...
6
votes
1answer
175 views

De-zephyr The Solution!

Here's another original chess problem of mine for you all to solve today! In the following position, White wants to stalemate Black even though they can win, for unknown, unclear, unexplained, and ...
11
votes
2answers
3k views

The grades of the students in a class

You are a new Math 102 professor in a university class of 88 students and would like to learn their grades from previous semester to know your students better and put a note of it to get an idea how ...
2
votes
0answers
84 views

The Switchup-2.0

This question from last year (which in itself was anticipated on CSE two years prior) has a complete switchup of all non-pawn pieces on the board. The idea is to optimize the amount of moves needed to ...
7
votes
0answers
189 views

An Unusual Amount Of Help

Another day, another helpmate to solve! Here's a really complicated one! The Black pawn on Black's first rank moves like a normal Black pawn. It's White to move first. Given that White moves to ...
1
vote
2answers
255 views

Minimize sum of guesses to win lottery

Ten boxes are given with $a_1,a_2,a_3,a_4,a_5 ......a_{10}$ number of balls in them respectively .These boxes are randomly ordered but $a_1,a_2 .....a_{10}$ is told.We can arbitrary select a box and ...
8
votes
2answers
328 views

Square Spin #4: Rude Awakening

Square Spin History: #1>#2>#3>#4 New Rule This puzzle introduces a new square type: Lonely squares (Ly) Lonely squares This type of square contains a box and it is ...
7
votes
2answers
228 views

A “Simple” Task

Here's a "simple" task for all of you solvers out there: With White to play first, and with both sides working together to checkmate White, aka a helpmate, what is the quickest way for Black to ...
5
votes
1answer
209 views

Square Spin #3: Hickory Dickory Dock

Square Spin History: #1>#2>#3 Recap of the Rules Basic rules from #1 Ambiguity, Un and Re squares from #2 Problem #3: Hickory Dickory Dock The mouse ran up the clock. ...but ...
8
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1answer
278 views

3D Chess - Stale NBA (kNight-Bishop Assault)

This is my very first chess puzzle. Any constructive feedback is more than welcome. Thanks! Introducing 3D Chess! To make things simple for the first time, we are using a $3\times3\times3$ ...
12
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4answers
519 views

Red and White Squares

There are two grid boards with the dimension of 9x9 and 14x14, consist of all white squares. You are supposed to color some squares with a red color on the conditions below: In a board, if two square ...
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3answers
138 views

Approximate this big number using a binomial [closed]

Mr. Magico is a greater believer in this number: $$2^{50}=1,125,899,906,842,624‬$$ He also like to play cards, although he isn't fussy about the size of his deck, and nor does he care how many ...
12
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5answers
758 views

Cup and Trade: The Perfect Nutmeg Soup

Your package from Orinoco has finally arrived! It's the Master Chef's Environmentally-Friendly Measuring Cup Set. It comes with 64 measuring cups having a volume of 1 cup, 1/2 cup, 1/3 cup, 1/4 cup, ....
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votes
2answers
255 views

Square Spin #2: Climb the Mountain!

Square Spin History: #1>#2 New Rules This puzzle introduces two new square types: Unmovable squares (Un) Replaceable squares (Re) Plus the concept of ambiguity! ...
6
votes
2answers
209 views

You Sign Me Right Round (Extended Edition)

I wanted to ask more questions about variations on This Problem. If you hadn't seen that one, check it out. It's required reading (and probably more fun). In the original problem, these were the ...
8
votes
2answers
222 views

You Sign Me Right Round

This is a 9x9 grid, with a sign in the center cell like shown. You can add signs to this grid one at a time following these rules: Each sign placed must point to the next sign placed Placed signs ...
5
votes
1answer
92 views

A Prime Length Rope into Prime length ropes

We have a rope with a prime unit length, and we need to divide this rope into $9$ ropes by cutting it with prime and/or 1 unit lengths. After cutting the rope, you are supposed to find any kind of ...
30
votes
6answers
3k views

Swapping rooks in a 4x4 board

You have a 4x4 chessboard with four black rooks on the top and four white rooks in the bottom. Your goal is to swap these rooks using the minimum number of steps. It does not matter which rook is ...
8
votes
2answers
722 views

Walk a Crooked Path

Here is a $7\times7$ board with three squares removed. You walk a path from square to square (adjacent horizontally or vertically), without visiting any square more than once. What is the most ...
6
votes
2answers
264 views

Savage Road Signs (Part 3)

You only need to have read Part 1 to understand this question, reading Part 2 will only help understanding the epic storyline. Your daughter refuses to talk to you even though you have (once more) ...
10
votes
1answer
370 views

Is this 3d Sudoku possible?

I was looking at images of 3d Sudoku's on Bing, because I was looking for a $9\times9\times9$ Sudoku, where each horizontal, vertical left-right and vertical top-bottom plane was also a Sudoku. ...
2
votes
1answer
113 views

Leveling up and Getting Items! v2

This is follow up question to Leveling up and Getting Items! You are playing an online RPG game with 9 friends of yours (10 people in total) and in the game, there is a 2-player dungeon where you ...
14
votes
4answers
2k views

Leveling up and Getting Items!

You are playing an online RPG game with 9 friends of yours (10 people in total) and in the game, there is a 2-player dungeon where you level up every time you enter and complete it. Only up to two ...
7
votes
4answers
293 views

Savage Road Signs (Part 2)

Please read part 1 or this might be confusing Since part 1, you have replaced the stolen stickers and your daughter has forgiven you. The highway ended up being a full 700km long, so you are happy ...
11
votes
4answers
2k views

Can you open the door or die?

You wake up and find yourself in a very strange room with a single door. You find a note on the ground surrounded by lots of cards: There are 66 green and 66 blue door cards on the ground. If you ...
11
votes
2answers
539 views

2019 gold coins to share

You and your friend has found in total 2019 gold coins in a treasure hunt. Since your friend found the place to dig up, he deserves a bit more gold than you so you offer a game to share the coins to ...
2
votes
1answer
94 views

A minimal stalemate with no possible illegal moves [duplicate]

Imagine that the main goal of the game of chess were to actually capture the opponent's king, not just checkmating him. So a stalemate would (usually) no longer be a draw, but a loss for the ...
2
votes
2answers
219 views

The Tiled Labyrinth Returns

This is a variant on The Tiled Labyrinth. The rules are the same, except that the goal has changed. You will probably want to use this script which was created for the initial puzzle but applies ...
13
votes
3answers
2k views

99 coins into the sacks

You have 99 coins that you need to place into any number of sacks. After doing so, you write on each one the number of sacks that are lighter than that sack. For example, if you put 98 coins into one ...
5
votes
1answer
133 views

Surviving the Zombie Apocalypse

It is the zombie apocalypse. Your car has limited fuel in it, and you will not be able to refill your tank once you run out. You are planning one final mission to gather supplies. You have identified ...
6
votes
2answers
358 views

Pawn Promotion Double Checks

In chess, it is possible to double check whilst giving promotion. An example of this would be a pawn promoting to a queen while a discovered attack from a rook behind the pawn checks the opponent’s ...
2
votes
2answers
110 views

Pawninos-44 Checks In A Row

Here’s a fun one! I call it Pawninos because the pawns, like dominos, all fall into a cycle! Start with an 8x8 chess board. Give black his king on h4 and no other material. Give white all of his 8 ...
19
votes
5answers
1k views

Island of Knights, Knaves and Spies

There is an island with $N$ inhabitants (for example $A_1, A_2, \dots, A_N$), each of them is either a knight, a knave, or a spy. As usual: knights will always tell the truth upon answering a ...
5
votes
1answer
171 views

Dragons and Dragon Slayers

In the Kingdom, there are 7 dragons and 7 dragon slayers. Each dragon has ($\text{index}\times10000$) hit points (i.e. $10,000\to70,000$). Each dragon slayer does ($\text{index}\times1000$) damage (i....
19
votes
5answers
638 views

Square Spin #1: Sun and Moon

Defining Square Spin Lets play a game! The aim of this game is to transform one image into another using the least amount of moves possible. Here is what a move consists of: ...
14
votes
1answer
450 views

Keeping a ball lost forever

Suppose you can make a rectangular maze, where each cell (apart from the bottom-right) can contain an arrow in one of the four directions (up, down, left or right) of your choosing, except for those ...
2
votes
3answers
182 views

Make the largest box from a cardboard sheet Chapter #2

Please see: Make the largest box from a cardboard sheet Thanks to his older brother's friends: @Oray, @Weather Vane and @mlk, the boy managed to make as large cardboard box as possible. Unfortunately,...