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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Weighing Coins -- a Different Approach
This is a question of my own devising. You have a double pan scale which will tell you whether 2 coins or 2 groups of coins weigh the same or whether one side is heavier than the other side. You have ...
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What is the maximum number of people who speak only 1 language?
There are 1000 people in a conference. 500 speak English, 500 speak Spanish and 500 speak Hindi. What can be the maximum number of people who speak only 1 language?
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Maximizing row and column products in a 4x4 grid
Using the numbers 1, 2, 3, ... 16 each exactly once, fill each square of a 4x4 grid so that the product of the numbers in each row is a multiple of $N$ and the product of the numbers in each column is ...
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Can black and white cooperatively put a stalemate to black in 16 moves (under ser-h conditions)?
ser-h=n – serial helpstalemate in n moves. Black execute n moves in a row, after that White execute a stalemate for bK.
Additional questions:
a) how many stalemates are possible under the same ...
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Destroying Democracy
There is a square grid of people and two political parties: Red and Yellow. The grid is split into districts, with the following rules:
All districts must be rectangles
Each voter must be in exactly ...
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8x8 grid with no unmarked L-pentomino
What is the minimum number of cells on a 8x8 chessboard that need to be marked so that the unmarked cells do not contain an L-pentomino?
An L-pentomino looks like
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Finding the 9 chapters
Suppose that you have a book of 1000 pages.
You know the book has 10 chapters and know each chapters has at least 10 pages, i.e., as chapter 1 starts at page 1, chapter 2 can only start at the page 11 ...
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Identical cubes in a sphere
Suppose that you have a sphere of radius 10cm. At most how many cubes of side 1cm can you fit in the sphere such that:
A cube can touch another cube (share a face, an edge or a point) but cannot ...
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Identical squares in a circle
Suppose that you have a circle of radius 10cm. How many squares of side 1cm can you fit at most in the circle such that:
A square can touch another square (share an edge or a point) but cannot ...
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How many uncoordinated cubers does it take to solve a Rubik's cube with multiple solutions?
Inspired by Rubik's cubes with multiple sets of colors or stickers. Suppose there's a Rubik's cube with multiple solutions (represented by multiple sets of colors) made with special paint that reflect ...
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What’s the highest salary the greedy king can arrange for himself?
A little kingdom contains 66 people, a king and 65 citizens. Each of them, including the king, has a salary of one gold piece. When democracy comes, the king is denied a vote, but he has the power to ...
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How to match pairs on raw tables?
The idea for the puzzle came from working with test score tables. In this case, the raw tables indicate an internal identifier that differs from user_id. To match, you have to download solutions and ...
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Visiting every digit
A clock uses a seven-segment display as following:
Each move involves adding or removing a single segment. Starting with the digit 0, what is the fewest number of moves needed to visit all the ...
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Balls of different weights: how few balls can there be?
This puzzle was inspired by the one in this posting by Hemant Agarwal.
There are n balls. Their weights are distinct positive integers which sum to W. The balls have the property that, if any one of ...
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Prisoners and warden game, again?
Source:
There are 100 prisoners in a prison. As usual, there is a warden who loves to play games, hence offers the prisoners a chance to free themselves.
He says
There is a room with a whiteboard, ...
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