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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Make the three products equal and as large as possible
Beginner puzzle
This puzzle is intended to be suitable for people who are new to puzzle solving.
Clarification: Both experienced solvers and new solvers are welcome to post solutions to this puzzle.
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75 integers are squared or cubed: minimum distinct results? [closed]
75 different integer numbers are written on a blackboard. Each is erased and replaced with either its square or its cube, the operation being random for each. What is the minimum quantity of different ...
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Two prisoners and twenty marbles
Two prisoners are planning their escape. Their cells are locked with a padlock that must be opened with a 5-digit code (numbers 00000 to 99999). Each prisoner knows the code of the other prisoner's ...
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Minimum number of questions for real treasure
There are 2000 treasures, among which only one is real and the others are fake. There are also 2000 knights, among whom one always tells the truth while the others always lie. You can ask the knights ...
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Approximate ln(2) out of small numbers
Given numbers 1,2,...n, the goal of this puzzle is to make a number as close to the mathematical constant $\ln(2) ≈ 0.69314718055$ as possible.
Rules
You can only use the four mathematical ...
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General attacking chessboard squares
This is a general version of this beautiful puzzle.
Place any number of standard chess pieces on a 8x8 chessboard, such that there is at least 1 empty square attacked by exactly 1 piece, at least 1 ...
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Fewest number of prisoners needed
You are an assistant to the king, who has scheduled a party tomorrow. There are 1000 wine bottles in the king's possession, and unfortunately, 3 of them are poisonous. Consuming from any of these ...
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New record for minimally clued 5x5 Hidato
CrSb0001 has been studying the minimum number of clues to force a unique solution in Hidato for variously sized boards. They came up with a 5x5 Hidato with 5 clues but it was found that it has ...
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Hexominos from pentominos, heptominos from hexominos
All twelve pentominoes can be obtained by attaching a single unit square (edge to edge) to one of the squares that make up one (or more) of the following four tetrominoes:
a) What is the least number ...
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What is the minimum amount of numbers needed to create a 4x4 Hidato with a unique solution?
Goal of Hidato:
Fill in a grid with a series of consecutive numbers that connect each other horizontally, vertically, or diagonally.
So I have been working on figuring out the minimum number of ...
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How long will it take for the horse to be captured?
Source: https://open.kattis.com/problems/ambush
Problem: When Farmer Oskar doesn’t watch his cows closely enough, they tend to wander off into the forest to hunt for horse spies. To catch an enemy ...
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An Amazing Configuration
Ed Pegg found in December 2019 this amazing configuration consisting of 22 points in 28 lines of 4.
On those points place 22 different positive integers such that the sum of any of the four points in ...
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Pythagorean pentagons
To follow up on the theme of so called "pythagorean" dissections, here is one more for you to chew on. I hope you don't get bored.
The pentagons above have sides respectively 3, 4 and 5.
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Maximum filled days
I have two types of items, $i_1$ and $i_2$. $i_1$ items can be used at most $50$ times and $i_2$ items can be used at most $120$ times.
I have $7000$ items $i_1$ and $800$ items $i_2$.
Each item $i\in ...
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Add rules to Minesweeper until you can start with nothing
Think of classic Minesweeper game, with the following list of restrictions on the placement of mines:
C (Connected): All mines are connected via 8-way neighborhood (orthogonal and diagonal).
Q (Quad):...
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