Questions tagged [optimization]
A mathematical puzzle where you have to optimize a certain objective function (maximize profit, minimize cost).
271
questions
5
votes
3answers
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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
votes
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
votes
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
votes
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
votes
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
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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
votes
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
votes
2answers
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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 ...
14
votes
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
votes
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
votes
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
votes
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 ...
0
votes
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
votes
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, ....
7
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,...
