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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prisoners riddle - a button, a light and a timer
Here is (yet another) prisoner riddle. I made it up (maybe it was asked before, but to the best of my knowledge I'm the first to ask it - correct me if I'm wrong).
There are 1000 prisoners who are ...
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Two triangles in a light bulb
Here’s a light bulb made of a regular dodecagon (yellow), two equilateral triangles (light gray), and a square (dark gray). Show that the red and blue triangles have the same area.
Of course, you can ...
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How many computers can be connected at once?
Netwalk (and other names) is a puzzle game with randomly generated "networks" consisting of computers (nodes), a source node, and connectors (either a straight through pipe, a right-angled ...
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Covering a rectangular floor with prime tiles
At my local store the only tiles sold are size 1 x p, p any of the first twenty five primes. What is the area of the largest rectangular floor, with width and height greater than 1, that I can ...
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Most symmetrical tangram
We discovered a new toy store near our house, and my daughter and I were very excited to check it out. We found a curious puzzle there and brought it home with us. After googling about it a bit, I ...
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The question contains the answer (literally)
How many ways to choose 3 letters from ONE? Answer: 1
How many ways to choose 1 letter from FOUR? Answer: 4
How many ways to choose 2 letters from SEVEN? Answer: 7
What is the largest n such ...
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How to select P so that the angle APB is as large as possible?
Given a line and two points A and B, which point P on the line forms the largest angle APB?
Bonus question: How should we select P so that the angle APB is as small as it can be?
P.S.
I tried solving ...
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Can we reach a stage where there are 105 piles with 1 tile in each pile?
You are given three piles with 5, 49 and 51 tiles respectively. Two operations are allowed:
merge two piles together or
divide a pile with an even number of tiles into two equal piles.
Is there a ...
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What is the minimum number of games played between Arun and Disha?
Arun and Disha played several games of table tennis. At five different points during the day, Arun calculated the percentage of the games played so far that he had won. The results of these ...
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The Seven Gods Problem -- an extension to "The Hardest Logic Puzzle Ever"(the three gods problem)
Seven Gods Problem: How do I identify each god's identity with the fewest questions?
Description of the Seven Gods Problem:
The Truth God always tells the truth.
The False God always lies.
The ...
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Beetles on a Chessboard
This question is taken from Problem-Solving Strategies by Arthur Engel.
The question says:
A beetle sits on each square of a 9 x 9 chessboard. At a signal each beetle crawls diagonally onto a ...
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Dividing both the interior and the boundary of a square into equal parts using polyominos
We want to cover an m×m square with n non-overlapping axis-parallel polyominos such that both the interior and the boundary of the square are divided into n equal areas and n equal lengths, ...
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Can you make a closed loop of interlocking chips with three notches?
Here's a circular chip with three evenly spaced notches. Two such chips can be attached as shown, where the "boundary circle" of each chip goes through the center of the other, and the ...
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Fewest cages for unique Killer Kropki-less Sudoku
Inspired by Why are these 5s and 1/9 forced in by this Killer Sudoku cage under Full Kropki rules?
What is the fewest number of cages needed for a Killer Krpoki Sudoku to have a unique solution?
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Minimum number of clues for a Find-the-stars puzzle
Previously I posted collections of my Find-the-stars puzzles here, here and here.
This post is different.
You are asked to create a puzzle.
Find-the-stars rules:
A Find-the-stars puzzle is played on ...
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Create a Distinct 5x5 Grid Using Only 3x3 Increments
This is a follow-up question to Different numbers in all cells of a 3x3 board v2
Here is the playable version.
You have a 5 × 5 grid whose entries all start at 0. A legal move is:
Select any 3 × 3 ...
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Puzzle Series: solve one to unlock the next [closed]
I've created a series of browser-based logic puzzles designed to be solved in sequence. Once you solve one puzzle correctly, you'll be automatically redirected to the next stage.
At the moment, there ...
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Moving multiplying cells away
At time T=0, a cell is placed at the origin. Every second, you can control the cell to divide once (one cell splits into two). After division, you can move the daughter cells one unit distance up, ...
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The Royal Relay on a Chessfield
Playable Version
In the ancient Kingdom of Gridoria, a mysterious curse has frozen the entire realm: every citizen, every castle, every mountain.
The royal court's only hope lies in a sacred Relay ...
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Shortest tour from a Bishopawn
A Bishopawn is here defined as a Bishop that can also advance one square, just like a Pawn. That means the Bishopawn can change its square color and visit all the squares!
What is the minimum number ...
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Prime and Alphabet Draws - Puzzling Stack Exchange
The first prime numbers are: 2, 3, 5, 7, 11, 13, 17, 19, 23, 31, ...
At step one, you will draw 2 letters complety at random among the 26 letters of the alphabet.
You might for instance draw: "A&...
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Minimum Crossed Knight Chess Tour
The Knight's Tour is a famous sequence of moves in a Chessboard.
We now search for a Knight Tour such that the number of intersections drawn by the tour is minimal.
Here is a valid Knight tour given ...
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USA and Africa have four types of frontiers!
For two different USA states the four possibilities happen considering their frontiers:
They don't share any frontier (e.g. Alaska and Utah or Florida and California)
They share a straight frontier (...
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Chess - Amazons - Magnus Carlen vs Gukesh 2025 Norway
Parts of this puzzle are taken from this nice puzzle of @Will.Octagon.Gibson.
An Amazon is a fairy chess piece that can move like a queen or a knight.
In this famous game at Norway in 2025, ...
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What is the maximum number of Amazons that can be placed on a 5x5 chessboard so that no piece attacks another?
An Amazon is a fairy chess piece that can move like a queen or a knight.
What is the maximum number of Amazons that can be placed on a 5x5 chessboard so that no piece attacks another?
Attribution:
...