Questions tagged [optimization]

A mathematical puzzle where you have to optimize a certain objective function (maximize profit, minimize cost).

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8
votes
4answers
777 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
178 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 ...
9
votes
1answer
596 views

Building a cheap road

The governor of Reniets (a land far, far away!) is known to be very stingy. He has to build a road which connects all the five cities in the region, which are oddly arranged on the vertices of a ...
6
votes
7answers
317 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 ...
24
votes
2answers
2k views

The tilted labyrinth - Can you find the fastest path in this 3D-puzzle? (Simulator now included.)

This is a puzzle was inspired by the board game labyrinth, which I very much enjoyed as a kid. It either requires very good 3D-visualization skills in your brain or some paper & scissors work. (...
5
votes
1answer
184 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
1answer
567 views

Blindfolded and disoriented near a space station

Following on from the recent blindfolded near the great Wall of China puzzle. Suppose you are floating in space a mile away from a huge space station (the death star perhaps). Assume that the death ...
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
1answer
436 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 ...
4
votes
2answers
173 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
247 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
615 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 ...
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 ...
10
votes
1answer
348 views

Minimize the intersection area

You are given two identical pieces of paper of size $a \times \sqrt{2} a$, like the standard DIN A4 paper. Put one paper on top of the other, such that none of the corners is under or above the other ...
6
votes
2answers
218 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 ...
9
votes
4answers
463 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
109 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 ...
30
votes
7answers
5k views

Dinosaur egg drop

Archeologists discover two dinosaur eggs, and you are given the chance to test the durability of these eggs (bad move on their part). Suppose that these eggs will absorb a specific amount of force ...
10
votes
5answers
896 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
209 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 ...
3
votes
2answers
334 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 ...
12
votes
1answer
770 views

What is the optimal first move in Mastermind?

For a given number of positions/holes and a given number of colors, which initial guess eliminates the most possibilities for the solution at a minimum? For 4 positions, it's AABB. What is it for 5, ...
8
votes
1answer
455 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 ...
10
votes
1answer
262 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. ...
2
votes
2answers
371 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 ...
9
votes
1answer
598 views

Maximize 'chains' in a Sudoku

Yet to be solved. Take 2 numbers such that $N, M \in \{1,2,3,4,5,6,7,8,9\}; N \ne M$. Start with a solved 9x9 Sudoku grid. Find any $N_1 = N$. Find an $M_1 = M$, in the same row as $N_1$. In the ...
20
votes
2answers
2k 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 ...
13
votes
1answer
397 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
2answers
649 views

Crystal Maze totem pole puzzle

The UK game show "The Crystal Maze" features a puzzle based around a totem pole. The contestant has four different coloured blocks which can be stacked up to make a totem pole. The blocks may be ...
7
votes
1answer
363 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 (...
8
votes
1answer
175 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 ...
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 ...
4
votes
1answer
201 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 ...
6
votes
3answers
328 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
3answers
258 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 ...
8
votes
1answer
343 views

Megan visits all the stations

The other day I was waiting for a train and had just popped into the nearby branch of Costa Bean for a coffee, when who should I run into but my old friend Megan and her partner Ricky, studying a ...
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
715 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
257 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
977 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 ...
1
vote
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 ...
9
votes
2answers
501 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 ...
8
votes
3answers
554 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 ...