Questions tagged [optimization]

A puzzle where you have to optimize a certain objective function (maximize profit, minimize cost). There should ideally be a provable best answer, to avoid making the puzzle into an [open-ended] game.

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2
votes
0answers
93 views

How old is Grandfather?

This position has been used in hundreds of chess problems for various reasons by a plethora of problemists over many, many decades. It is known as "Vielväterstellung" in German, or "The ...
10
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2answers
411 views

Transform a pile of cards in reverse order

There are 52 cards on a table and numbered in order from 1 to 52 with number 1 on top. The following operation can be repeatedly done: split the pile into two piles without shuffling and take cards ...
8
votes
2answers
894 views

Five positive integers in a row, each being the sum of the digit sum of its neighbours

Five positive integers should be put in a row such that each integer is the sum of the digit sum of its neighbours. The integers at the beginning and at the end have only one neighbour, i.e the first ...
5
votes
3answers
375 views

100 prisoners and a secret number (sequel)

Inspired by this brilliant puzzle by @DmitryKamenetsky! Much to the annoyance of the guards, the sly prisoners bribed a guard and learnt about the number in the envelope in advance, and the first ...
11
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3answers
1k views

Find an integer where each sum of 5 consecutive digits is prime

Find the largest positive integer with the following properties: every sum of 5 neighboring digits in its decimal representation is a prime number. those prime numbers get smaller and smaller from ...
12
votes
6answers
1k views

How many bottles can you drink?

You have 120 bottles of Cola and 120 bottles of Sprite. You can exchange 3 empty Cola bottles for a new bottle of Sprite. You can exchange 4 empty Sprite bottles for a new bottle of Cola. You can ...
1
vote
3answers
464 views

The Third Hardest Logic Puzzle in the World

This puzzle is heavily derived from the Second Hardest Logic Puzzle in the World, which I also created. The current puzzle and the aforementioned are not identical, however. You have 5 guards: one ...
21
votes
7answers
4k views

Can you irrigate your lawn with 23 sprinklers?

You have a perfectly circular lawn with radius exactly 4 metres. Lately the grass has been turning yellow and quite rough, so you go to Stiv's Diabolical Instruments and describe your problem. "...
3
votes
3answers
299 views

Chess Construction Challenge #9: Two Eggs & A Flood

I have an odd idea for this challenge. It involves a very specific proof game construction. So pay attention! Given that: White and Black cannot move more than one pawn each throughout the entire ...
5
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2answers
599 views

A school needs a talented student (covering the hamming graph H(3,15) with closed balls of radius 5)

Assume a standardized test has $15$ multiple choice questions, with $3$ options each. A school has some students and wishes for at least one of the students to get $10$ correct answers. Since no one ...
3
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1answer
122 views

Chess Construction Challenge #8: Three Times The Charm

On a chessboard, a piece has a set number of legal moves. It can range from 0 to 27. However, this amount can also restricted. My previous questions have covered n=1 and n=2, it is time for n=3! Given ...
6
votes
3answers
414 views

Generalization of the two-surgeons-two-patients-and-two-gloves puzzle

This is the original puzzle with $n=2$. I recommend solving it before this one to get acquainted with the mechanisms. There are $n$ patients in an hospital (let's call them $p_1 \dots p_n$), each of ...
8
votes
2answers
213 views

Making 100 starting with two 1s

You have an empty blackboard. At each step, you can either write two ones on the blackboard, or erase two copies of a number n and replace them with n−1 and n+1. What is the fewest number of steps it ...
7
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3answers
497 views

Chess Construction Challenge #7: Double The Fun

Many thanks goes to @Retudin in a comment on my last question for this idea. In a chess position, pieces can be restricted as to how many moves they can legally make in theory. Since my previous ...
9
votes
5answers
1k views

Chess Construction Challenge #6: The One Move Royale

In chess, it is possible for a piece to have only one legal move. For example, in this position, the Black king can move only to h2. Given that: All 32 pieces are available for use. Construct: A ...
8
votes
1answer
444 views

Jumping token on a grid

A token starts at location (0,0) on an infinite grid. On turn $n$ it must jump $n$ units horizontally or vertically, in one of four directions. What is the least number of turns needed for it to reach ...
10
votes
2answers
323 views

Gentrification in Chessshire

You can skip the back story and directly jump to the question. Capitalism has arrived in suburban Chesster the community most famed for The Game, and with a vengeance. Rents have trebled in less than ...
6
votes
1answer
369 views

Discounts in a shop

I came across this sign in a shop and thought it could make a nice puzzle. So you can buy items and get discounts depending on how many items you got. You can combine discounts and use as many as you ...
22
votes
7answers
2k views

What is the minimum number of helpers that an explorer need to cross the desert?

There is a desert which can be crossed only by walking and this takes six days. The explorers of the desert can carry at most four days' water and food. If they want, they can take helpers with them. ...
3
votes
1answer
108 views

Mix a 2x2 Rubik’s cube

What is the minimum number of 1/4 turns of a solved 2x2 Rubik’s cube, such that no face will have two tiles of the same color? (I do not have this puzzle’s solution.)
1
vote
1answer
183 views

Catch the fugitive

The fugitive is at the origin. He moves at a speed of 100. You have a guard at every integer coordinate except the origin. A guard's speed is 1. The fugitive and your guards move simultaneously and ...
5
votes
3answers
271 views

The vaccine distribution conundrum

The context is that of a pandemic that is spreading wildly and requiring global vaccination of the population. You are working in a distribution center for the vaccines. One day you have been ...
20
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2answers
1k views

Beans under the chessboard

Under every grid cell of a chessboard, I put either one bean or nothing. Now if you choose a (grid) rectangular area on the chessboard, then I will tell you the parity of the number of beans under ...
2
votes
1answer
108 views

Fetching Alchemist, Excavation I

This is a puzzle in the Fetching Alchemist series. It has been generated especially for Puzzling Stack Exchange. Please note that, in my opinion, imperfect solutions should be up-voted so long as they ...
0
votes
1answer
74 views

Fetching Alchemist, Grand Potion I

This is a puzzle in the Fetching Alchemist series. There's no selling in this puzzle, just one potion to brew, but with a lot of ingredients. Please note that, in my opinion, imperfect solutions ...
2
votes
3answers
195 views

Advanced Fetching Alchemist II

This is a puzzle in the Fetching Alchemist series. From now on, you complete quests at the place you start at as well. Please note that, in my opinion, imperfect solutions should be up-voted so long ...
2
votes
1answer
100 views

Advanced Fetching Alchemist I

This follows the same rules as previous Fetching Alchemist puzzles, except you choose where you start, and you may now return to your starting place after leaving it. How to Play You are looking for ...
10
votes
2answers
573 views

Adding coins inside a ring of coins

17 identical coins with diameter 1 are lying flat on a table, such that their midpoints build the vertices of a regular 17-gon (regular heptadecagon) and adjacent coins touch each other. What is the ...
0
votes
0answers
59 views

Grids with tiles of two colors and connectors

Make a square grid with an even side. Make a continuous trail which passes through all small squares; the trail ends where it started. Where there is an angle you can put a red or a blue tile. On ...
5
votes
3answers
176 views

Numbers with minimal sum at the vertices of a cube

The eight vertices of a cube are marked with numbers from 1 to 8 such that the sum of any three numbers on any face is not less than 10. What is the minimum sum of the four numbers on a face?
4
votes
1answer
73 views

A 4x6 grid with adjacent integers with gcd > 1

You are given a 4x6 square grid. Each square of the grid should be filled with different positive integers. The gcd (greatest common divisor) of any two adjacent (horizontally or vertically) squares ...
3
votes
3answers
264 views

Not selling 100 pencils

A shop sells pencils only in boxes of fixed size. It cannot sell 100 pencils. It can sell any larger amount of pencils. It has one of each size box on display. question 1: What is the minimum amount ...
3
votes
1answer
73 views

Divisors ending with digits 0-9 each

What is the smallest positive integer, which has - for each of the digit 0-9 - a divisor ending with this digit?
8
votes
5answers
1k views

Minimize 1×3 tiles on a 5×5 table to block any more 1×3 tiles

What is the minimum number of 1×3 tiles that can be put on a 5×5 table so that no more 1×3 tiles can be put on it? Borders of a tiles are parallel to sides of the table. It is 5 but I can not prove ...
2
votes
2answers
356 views

Traffic light controller

Consider the following diagram. Once every 2 seconds a car enters from the top and travels down towards the exit. Once every 3 seconds a car enters from the left and travels to the right exit. In the ...
9
votes
1answer
157 views

Interchanging knights and rooks… again!

Is it possible to interchange the positions of the the two black knights and two black rooks with those of the two white knights and two white rooks? Movements allowed are those of the corresponding ...
10
votes
2answers
599 views

Two football teams

Twenty two football players have agreed to split every week into two teams and play a match against each other. Every week, teams will be chosen differently, 11 players in each team, and they will ...
16
votes
7answers
2k views

Flashlight and 8 batteries

A flashlight requires 2 AA-type batteries to operate. Both these batteries need to be charged for the flashlight to provide light. We happen to have 8 batteries, but 4 of them are charged while the ...
5
votes
1answer
244 views

Looking for Navigators for the Famous Vega Classic

Do you have what it takes to compete in the famous Vega Classic? Looking for skilled navigators. Apply below. You have a craft that is capable of 10m/s$^2$ acceleration in any direction, and we're ...
0
votes
1answer
100 views

Trail passing through squares of a grid

Let's construct a 10x10 grid. 0n the 100 squares you are allowed to place 7 bases (the red dots in the diagram below) in any square on the grid. Then you fill the grid with skinny trominoes. The ...
8
votes
2answers
449 views

Most Complicated Illegal Partial State of Rubik’s Cube

This puzzle is a follow-up for Does The Rubik’s Cube In This Painting Have A Solved State? What is the most complicated illegal “partial state” possible for a Rubik’s Cube? To be more specific: a ...
1
vote
1answer
87 views

How to arrange a set of cubes to get a tower of two?

The puzzle is as follows: Assume that you have this peculiar toy. This toy is composed by many plastic pieces which is shown in the figure from below, all of them are cubes. You can use as many as ...
10
votes
2answers
695 views

Never kill your king … without first seeking proper legal advice!

This is a follow-up to (Almost) all hands on check by @loopy walt. The task (mate in one with as many essential pieces as possible) stays the same, but you are to go about it more cunningly. Recap of ...
7
votes
4answers
2k views

How can you get 13 pounds of coffee by using all three weights each trial?

The puzzle is as follows [with minor copy edits for grammar]: A merchant has a kiosk nearby our market. He has a sack of 52 pounds of coffee to sell. Assuming that he only uses a two pan scale and ...
4
votes
2answers
451 views

Maximum number of masses you can weigh given 3 weights

The puzzle is as follows: Assume that you have a two pan scale and three weights, one of 1 pound, the other 3 pounds and the last one 9 pounds. How many objects of different weights can you weigh at ...
0
votes
1answer
63 views

How can you use a two pan scale to find which coin is counterfeited? [duplicate]

The puzzle is as follows: Detective Mike has four bags with 100 coins of one cent each. All of these coins have the weight with the exception of one coin which weighs a little less than the rest ...
2
votes
1answer
270 views

Arrange candies without repeating pattern

The following puzzle had been posted before but I couldn't understand the only answer that was given there, which was by @neodne . So, I created this post asking someone to explain neodne's answer to ...
8
votes
3answers
976 views

(Almost) all hands on check

Historical note (skip if you like): In this interesting puzzle @TSLF asks for the "maximum number of black and white pieces that are involved in a checkmate position". Originally, they left ...
5
votes
1answer
266 views

Four queens on public transport

The enlightened but, sadly, fictional country of Switzerland has it all: A strong democracy that resists centralism, a reliable public transport network and its own version of chess. Swiss chess ...
7
votes
3answers
412 views

Proving by weighting

Here is the puzzle: Alice and Bob leave in a world where all diamonds are divided into 2 types: Light and Heavy. All diamonds look exactly the same. All light diamonds weight exactly the same, all ...

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