Questions tagged [optimization]
A mathematical puzzle where you have to optimize a certain objective function (maximize profit, minimize cost).
253
questions
4
votes
0answers
86 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 ...
2
votes
0answers
112 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 ...
7
votes
2answers
258 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
180 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 ...
6
votes
1answer
189 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
260 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
459 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
125 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
735 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
225 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!
...
5
votes
1answer
146 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
197 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
76 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 ...
28
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
712 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
254 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
247 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
104 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
282 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
519 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
76 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
201 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
129 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
347 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
105 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
156 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
560 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
437 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
176 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,...
8
votes
4answers
774 views
Make the largest box from a cardboard sheet
A boy in order to tidy his room asks his parents for a cardboard box to store lots of small toys. Unfortunately they didn't find any but only a raw cardboard sheet of dimensions ...
2
votes
1answer
174 views
Tokyo Metro puzzle special #2: The tour of the Metro
This is a simpler puzzle: How many stations do you have to pass by to pass by every station of the Metro? map
Please either 1) explain your solution or 2) make an image of the route. Once consensus ...
6
votes
7answers
316 views
Find minimum number of meeting periods to reach 2 degrees of separation for a group [closed]
I am running a training course and I want to arrange a set of 1:1 meeting periods between the participants such that at the end of the day there is a maximum of 2 degrees of separation between any of ...
5
votes
1answer
177 views
What is the optimal way to play standard Battleship?
I've seen the questions on this site with modified Battleship, but I haven't seen one for the standard variation.
So - what is the optimal strategy to win this game?
11
votes
4answers
305 views
Distinct Arrangements of Balls on Tiles
You want to put several balls on $8 \times 8$ tiles, such that all $16$ ball arrangements on its rows and columns are different. What is the minimum number of balls to be put?
Two arrangements of ...
3
votes
2answers
185 views
Should I Rest at the Travelator or Not at the Travelator?
This is a real-life puzzle encountered by one of my friends, again.
After landing and arriving at the airport, I want to pick my baggage up quickly. The problem is that the baggage claim is $500$ m ...
4
votes
2answers
170 views
Optimal guess in a game
Suppose that A and B play a strange game. At the beginning of the game A can choose one real number - $x$ - between $0$ and $60$. Each round of the game goes like this:
B names random real number $b$ ...
9
votes
3answers
2k views
Folding a paper wouldn't be this hard
Alice and Bob started to play a game with a piece of A4 paper. Alice is going to cut that paper as she wants and will give it to Bob, then Bob will fold the paper from anywhere he wants. In the game, ...
5
votes
3answers
243 views
Fill $N$ by $M$ grid with numbers in such a way that any given cells' neighbors are different
Create an $N$ by $M$ grid with numbers in such a way that satisfies following conditions:
numbers should be integers that range from $1$ to $r$.
for any cell $C$, all its adjacent neighbors (i.e. ...
3
votes
3answers
1k views
Three coins for the fair king [duplicate]
Based on the question Eight coins for the fair king:
I saw a comment saying "There isn't a good solution known even with three coins in all cases".
So the challenge here is to try to solve the same ...
47
votes
6answers
4k views
Eight coins for the fair king
You are responsible for creating new types of coins for the court.
King respects the forgetful: he wants you to create 8 coins of different value, no more.
King respects the feeble: he wants that any ...
5
votes
3answers
613 views
Should I kill all of my elves?
I've been playing a simplified variant of The Great Elf Game for a few days now and I'm struggling to identify an optimal strategy.
Rules:
You start with 12 elves. Each elf is sent to gather a tree ...
6
votes
4answers
2k views
Coloring the Chess Board
We have 8x8 Chess board like grid (8x8 2D matrix) and we are trying to color every single square/cell. But the rules are interesting;
You may start from any square you want and color that square for ...
9
votes
4answers
454 views
Cupcake division
A elementary school student brought cupcakes to their class to celebrate their birthday! However, there's a problem: There are 25 students in the classroom, and only 24 cupcakes!
The students have ...
-1
votes
1answer
107 views
Annual Meet Puzzle
The annual meet was attended by 20 persons. The persons who attended the meet have worked in eight different firms – M, BC, K, A, BA, D, PC and E.
The following table provides information about the ...
6
votes
2answers
209 views
The Minimized Dropmate
I don't know, but I think my opponent just may be cheating in this chess game.
So, the natural thing to do is cheat right back! My plan is to put black pieces on the board so the white king is ...
4
votes
1answer
391 views
Are there basic weighing puzzles requiring adaptive strategies?
Let us define a basic weighing puzzle as such:
There are <number> identical balls, except one weighs <more/less/a different amount than the others>
A balance scale may be used to weigh two ...
