Questions tagged [optimization]
A mathematical puzzle where you have to optimize a certain objective function (maximize profit, minimize cost).
17
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
136 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....
14
votes
1answer
410 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
166 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
760 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
159 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
308 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
162 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?
7
votes
3answers
209 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
178 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
163 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 $b$ ...
8
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
210 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 ...
46
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
603 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
449 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
105 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
190 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
190 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 ...
10
votes
5answers
843 views
Optimize a keyboard for one-finger typing
The ubiquitous QWERTY keyboard layout works well enough for ten-finger touch typing (though Dvorak proponents may disagree).
But what if you're typing a text message on a mobile phone? Those fiddly ...
8
votes
1answer
207 views
Create your own custom ruler
There is a blank ruler of $X$ units. You are going to set $9$ marks on this ruler so that you will be able to measure all integer values from $1$ to $X$ units with only one measurement.
What is the ...
12
votes
3answers
2k views
Removing 100 digits from the first 100 numbers
Write the first 100 positive integers next to each other to form one big number: $$123456789101112131415161718192021\dots90919293949596979899100.$$ If we remove 100 digits (not necessarily consecutive)...
13
votes
4answers
3k views
A dice game, what is the optimal strategy?
Alice was walking on the street when she came across a man playing with a die. She could not help trying to check if the die was loaded and while she was concluding that it wasn't loaded, the man ...
8
votes
1answer
452 views
Clearing the Robot Museum
The grand opening of the Collapsible Robot Museum is just 1 week away in the robot nation of Robotia. The museum is unique because shortly after the museum closes, the building collapses into a flat ...
3
votes
2answers
333 views
Rectangles and Diagonals
A 4×4 table has 18 lines, consisting of the 4 rows, the 4 columns, 5 diagonals running from southwest to northeast, and 5 diagonals running from northwest to southeast. A diagonal may have 2, 3 or 4 ...
2
votes
2answers
341 views
33 stones into gold transmuter
There is a magic transmuter which turns stones into the gold! But this transmuter works weird.
Every time you put a stone or more stones and press a button, it takes that stone into a slot in the ...
10
votes
1answer
256 views
Barrel - Part 3
An entry in Fortnightly Topic Challenge #35: Restricted Title 1. Title based on this xkcd.
This is a continuation of Barrel - Part 1 and Barrel - Part 2, but this puzzle is still self-contained.
...
13
votes
1answer
392 views
Candy Button Paper
An entry in Fortnightly Topic Challenge #35: Restricted Title 1. Title based on this xkcd.
Your biggest dream has come true: you have an infinite supply of your favorite five-flavor candy button ...
6
votes
1answer
354 views
Red Fish Blue ꟻish
You are presented the following six cards.
The red cards are rotations of F, and the blue cards are rotations of ꟻ (backwards F). Your goal is to make it so that the red cards are rotations of ꟻ (...
19
votes
2answers
1k views
A thirsty king and his knights
The black king has spent his life fighting over this strange checkered land, the white king has finally been defeated and his troops have surrendered and pledged allegiance to him. Now he's not sure ...
8
votes
1answer
172 views
Mitosis of 80 bioelectronic cells
You are working in a bio-laboratory, where they produce some special bioelectronic cells which have mitosis ability.
FYI: Mitosis is a process of cell duplication during which one cell gives rise to ...
4
votes
1answer
191 views
Find the fake bar in 2 weighing [duplicate]
You are given 8 equal sized bars of silver labeled a to h. You know for a fact one of them is fake, and the only measurable difference is weight. However you do not know if the fake bar is heavier or ...
9
votes
6answers
1k views
Optimizing month abbreviation to number
(This comes from a real-world requirement.)
The idea is easy - if you have the three-letter abbreviated name of a month, say "Jan", get the numeric month number (for "Jan", 1). Sure, sure, pick a ...
5
votes
3answers
254 views
Crazy queen in checkers
Checkers
Checkers, also called draughts, is an interesting game. all pieces are placed on black tile and are all pawns at the start. When a pawn reach the final line, a powerful piece is created: the ...
6
votes
3answers
322 views
5 Tires with maximum distance
I just bought a car with $5$ identical tires on it, as you guess $4$ of them were already installed, just one is in the trunk.
The seller said that while the tires on the front, they can go $48k$ ...
5
votes
1answer
2k views
Is there only one solution to the “Ten Penny Puzzle” or more?
Not knowing the dimensions of the square in the Ten Penny Puzzle I ask if there is more than one unique solution that isn't a reflection/mirror of the one shown in the video, if you know the ...
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
709 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
244 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
948 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 ...
9
votes
2answers
491 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 ...
1
vote
1answer
268 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 ...
8
votes
3answers
545 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
146 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 ...
7
votes
2answers
400 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 ...
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 ...
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 ...
