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# 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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18 votes
3 answers
948 views

### PSE Advent Calendar 2023 (Day 8): A Quilt for Santa

This puzzle is part of the Puzzling Stack Exchange Advent Calendar 2023. The accepted answer to this question will be awarded a bounty worth 50 reputation.< Previous Door Next Door > Mrs. Claus ...
5 votes
2 answers
571 views

### Can you employ all 26 letters using three 11-letter, three 10-letter, or three 9-letter words?

I'd like to take the premise of my previous (and insofar, only other) post and extend it. Are there any wordsets that cover all 26 letters across... Three 11-letter words, Three 10-letter words, or ...
10 votes
4 answers
396 views

### Irregularly Deposited Compound Interest

Suppose you have a very peculiar bank account that obeys the following rules: The account pays 10% interest per year, generated continuously. Interest from the account does not compound automatically;...
• 2,544
7 votes
2 answers
2k views

### Three 8-letter words with at least 23 different letters

I have literally dozens of wordsets containing 22 different letters, but haven't been able to crack 23, and DEFINITELY not 24. Can you do it? Here are as many of mine as I feel like posting, to get ...
0 votes
1 answer
85 views

### Minimum function optimization puzzle #4: Using negative numbers?

Previous puzzle Take this puzzle of mine that I created around a week ago: Take these 3 functions: $f(x):=x+8,g(x):=x^2-3,h(x):=\sqrt x$ Starting from $x=0$,\color{black}{\text{How many times will ...
• 2,241
2 votes
1 answer
193 views

### Crossing desert with smallest amount of water [duplicate]

A man who lives in a desert sends his servant out to collect the flag which is 4 miles away from the man's home. To survive the servant must drink 1 litre of water on every mile he walks (so the ...
5 votes
1 answer
805 views

### Minimum number of turns

You have 64 identical-looking boxes numbered from 1 to 64, each weighing a distinct amount. On a turn, you can tell your friend two numbers between 1 and 64, and she will tell you which of the ...
• 336
6 votes
1 answer
254 views

### Minimum keystrokes

This puzzle is created by me. String 1: ...
• 1,491
0 votes
2 answers
135 views

### Minimum function optimization puzzle #3: 3 functions

Previous puzzle Take this puzzle of mine I created recently: Let $f(x)=x+1$, $g(x)=x^2-1$, $h(x)=2x-4$. Starting with $x=0$ and applying these functions as needed, what is the minimum amount of times ...
• 2,241
0 votes
2 answers
109 views

### Minimum function optimization puzzle #2

Previous puzzle Take this puzzle of mine I created about an hour ago Take two functions, $f(x):=x^2$ and $g(x):=x-3$. Starting from $x=0$ and applying these functions as needed, what is the minimum ...
• 2,241
1 vote
1 answer
176 views

### Is my solution to a mathematics puzzle I created the most efficient solution there is to it?

Here's a puzzle of mine that I created around 2 hours ago: Let $f(x):=x^2$ and $g(x):=x-4$. Starting with x=0, what is the least amount of times you need to apply the functions $f$ and $g$ so that at ...
• 2,241
2 votes
3 answers
404 views

### Button multi arm bandit problem

Let's say you have the following buttons to press, labeled a - j, that would earn you the following amounts of money: a: \$6 b: \$9 c: \$15 d: \$26 e: \$45 f: \$78 g: \$136 h: \$416 i: \$728 j: \$...
-3 votes
2 answers
207 views

### Improving Judgement pill problem [closed]

Lets say there are 10 different pills that improve or impair judgement each assigned a rating (1-10) of increasing or impairing your judgement (1 stupid, 5 normal, 10 super smart) You currently know ...
9 votes
1 answer
400 views

### Fitting snakes in a cage

11 snakes are in a 6x11 rectangular cage (grid) in a zoo. Each snake is a different length, from 1 to 11. No snakes may overlap. No spaces are empty. Each of the 6 rows may contain at most 2 snake ...
• 26.9k
10 votes
3 answers
2k views

### Minimal unsolvable minesweeper

I'm playing minesweeper on an infinite grid. I'm told upfront how many mines there are. What's the smallest possible $n$ for which there exists a configuration of $n$ mines such that, no matter where ...
• 1,536
5 votes
0 answers
255 views

• 6,498
25 votes
5 answers
2k views

### Colouring a rug

I have a rectangular rug in my living room composed of coloured patches (shown below). For convenience I have labelled each distinct colour from 1 to 6. Let's suppose that it was created by starting ...
19 votes
3 answers
2k views

### Playing Mastermind against an angel and the devil

This puzzle is based on a card game. There are 7 suspects and 3 of them committed a crime. The game contains 35 cards that contain the 35 possible choices of 3 out of the 7 suspects. One card is drawn ...
• 1,823
0 votes
0 answers
144 views

### Maximize an Nx7 rectangle of words step-by-step

In Scrabble, you score points for each new word you make on your turn. Therefore, on a board of AIRLINE and holding a rack of ...
• 1,237
8 votes
1 answer
616 views

### Rolling tetrahedra

The image below depicts a number of tetrahedral dice sporting face colors of red, yellow, blue, and green in a consistent orientation. These dice exist on a triangular tessellation of the plane, and ...
• 2,379
4 votes
2 answers
313 views

### Waffleing my Egg

This morning I had a waffle and a fried egg for breakfast. The fried egg was cooked with a mold, so it was perfectly round and three inches in diameter. The waffle was a 3-inch by 4-inch grid of one ...
• 8,206
9 votes
5 answers
602 views

### Minimum K for detecting fake pearls in one weighing

There are 10 boxes, each with the same number of pearls (represented by K). Genuine pearls weigh 30g each, while fake pearls weigh 29g each. Each box is either all genuine or all fake, and any number ...
• 938
129 votes
5 answers
142k views

### Is this duplo train track under too much tension?

My kids were making this train track of duplo the other day, and this is what they put together. They are still very young, and for them, this is something big. They were really proud that they ...
• 5,206
-4 votes
1 answer
202 views

### Find the Rat in the Hole

A rat is in one of 100 holes that are in a line. Each night he moves to the left or right 0,1, or 2 holes randomly selected. You pick one hole each day to look in until you find him. What procedure ...
• 625
13 votes
2 answers
482 views

### Minimum lines needed to draw the 12 pentominoes

You need 4 lines to draw the monomino and the same for the domino You can draw the 2 trominoes with 7 lines For the five tetrominoes I could do it first with 16 lines Then 15 lines And my best try ...
0 votes
0 answers
74 views

### Find the largest number with unique digits, that is divisible by each of its digits [duplicate]

Find the largest number with unique digits, that is divisible by each of its digits. For example 132 has unique digits and is divisible by 1, 2 and 3. But it is not the largest such number. Can you ...
10 votes
2 answers
667 views

### Pay each amount with at most two coins

Euro cent coins come in the denominations 1, 2, 5, 10, 20 and 50 cents. You are inconvenienced by the fact that you need a lot of coins to pay each amount up to 100 cents. To pay 99 cents, you need 6 ...
• 103
1 vote
1 answer
192 views

### Visiting all strings by swapping

Consider the following strings ...
• 7,845
7 votes
1 answer
366 views

### Prime Twelve Apostles

You are given an empty square grid. Each cell can be an island with a positive integer $n$ or a bridge connecting islands. The following rules apply: Each island with a number $n$ must have exactly \$...
5 votes
1 answer
325 views

### Maximize "sudoku" occurrences in a sudoku

How often at most can "Sudoku" occur in a valid (9x9) sudoku? create a valid sudoku replace (all occurrences of) 5 of the numbers by the 5 letters in "sudoku". (and leave the ...
• 8,939
11 votes
6 answers
2k views

### The shorter the message, the larger the prize (version II)

This is a successor question to The shorter the message, the larger the prize . For completeness I will include the entire question even though only the numbers have changed. Solutions to this puzzle ...
• 7,845
14 votes
1 answer
1k views

### The shorter the message, the larger the prize

Andrei and Belle have been set a task by their “friend”, Carroll. Carroll has promised them money depending on how well they do. Carroll will give a 99 bit array to Andrei and a different one to ...
• 7,845
5 votes
2 answers
573 views

### Largest binary rectangle without any arithmetic progressions

What is the largest rectangular grid (by area) that you can color in red and blue such that there is no red cell halfway between two red cells and no blue cell halfway between two blue cells, moving ...
4 votes
1 answer
230 views

### A special binary string

I was inspired by this puzzle. What is the longest binary string of "0" and "1" you can form such that no "0" is halfway between two other "0" and no "1&...
3 votes
1 answer
165 views

### Lowest possible ratio of number of borders to countries annexable

There's been a recent trend on Reddit of finding how many countries can be colored in by: Coloring nation a. Coloring b nations, those touching a's borders. Coloring c nations, those touching b's ...
• 8,263
26 votes
7 answers
2k views

### Approximate pi out of small numbers

Given the numbers 1, 2, ..., n the puzzle is to try to make a number as close as possible to pi using only the four mathematical operations +, -, *, / and parentheses (brackets). You don't have to use ...
• 7,845
5 votes
1 answer
337 views

### Nuts and screws

Imagine that you are given a box with n nuts and n screws. Each screw have different size (diameter) and on each screw there is ...
• 263
2 votes
0 answers
149 views

### Trippples - optimisation [closed]

Trippples Introduction Tripples (BGG) is a board game from the 1970s. It is played on an 8x8 grid, and each tile on that grid (except the corner starting tiles, and four blank tiles) contain three ...
• 1,013
11 votes
5 answers
2k views

### Green Triangles Puzzle

This question is closely related to Green Hexagons Puzzle. Start by choosing some triangles to be green. If a triangle is sharing an edge with at least 2 green triangles, it becomes green. This ...
• 689
7 votes
2 answers
1k views

### Green Hexagons Puzzle

Start by choosing some hexagons to be green. If a hexagon is touching at least 3 green hexagons, it becomes green. This repeats for as long as possible. What's the minimal number of initial green ...
• 689
1 vote
3 answers
440 views

### The secretary problem goes on budget

Secretary problem describes a scenario where a company wants to hire the best secretary from sequential interviews of candidates that can be done only once. In budget secretary problem a company has ...
6 votes
1 answer
667 views

### Cable with mixed wires

Let's say you have a cable that has n wires. Each wire on the left side corresponds to one wire on the right side. However you cannot distinguish between the wires ...
• 263
12 votes
3 answers
4k views

### I Hate Traffic And So Do You

I need to travel through the city from my house to school, but the traffic is horrible right now. I can only move along the city's grid with the following conditions: • blocks with traffic (marked in ...
• 574
8 votes
3 answers
618 views

### Cutting a square into integer triangles

You are given a square piece of paper with size 10x10 units. What is the most number of triangles that can be cut from this square, such that: Each triangle has integer sides. Each triangle is ...
6 votes
2 answers
282 views

### Kingly Laziness

What is the minimum effort the White king must put into arriving at this destination? His Majesty is not feeling productive today. This position was composed by Gianni Donati and published in Phénix ...
• 8,263