Questions tagged [optimization]

A mathematical puzzle where you have to optimize a certain objective function (maximize profit, minimize cost).

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14
votes
2answers
1k views

How many clues are required to ensure Einstein's Puzzle is solvable?

I used to play Einstein's puzzles a lot when I was younger, and very quickly learned to assess quite rapidly whether I thought a puzzle would be a quick solve or more time-consuming, but I never ...
1
vote
1answer
245 views

Find the optimal dot configuration

Rules: You have 9 dots, labeled A through I. You choose a layout (arrangement) for the 9 dots. You must connect the 9 dots with straight lines (no curves or extra lines). The object is to ...
10
votes
5answers
815 views

Houses in a grid

You are a city planner tasked with the placement of unit-square-sized houses in a rectangular-grid allotment, the size of which is up to you but must be as small as possible to save money. The number ...
2
votes
2answers
227 views

Is there a better solution to parallel segments problem?

There is a puzzle: Find a finite set of points with the following property: 1. Points are placed in space (not on a single plane) 2. If you take any pair of points A and B there are different ...
1
vote
1answer
459 views

Slot Machine Challenge

Karen owns a restaurant/bar. She wants to attract more customers, and is building her own custom slot machine game, which she can use to give away free drinks or prizes. The more a customer spends, ...
3
votes
4answers
718 views

Another poisoned bottle question!

There are $1000$ bottles of wine, of which $n\leq10$ are poisoned at random. (You don't know the exact number) A person consuming the poison dies on the midnight of that day. You have $2$ prisoners ...
2
votes
1answer
204 views

Shutting down all lamps [closed]

I found this problem from http://artofproblemsolving.com/community/c163h564755p3301930 . I have $n=2017$ lamps in a circle, and enumerated by $L_1,\ldots,L_n$. Some of them are switched on and some ...
7
votes
4answers
1k views

Minimum cells to fill grid without consecutive neighbours

Imagine you have a m x n grid which is initially colored white. you can fill in a cell with black color if and only if there are no immediately neighboring black cells (no black cells to the left/...
4
votes
3answers
410 views

$n$ monsters and $n$ people

There are $n$ monsters (M) and $n$ people (P) on the left side of a river. Nobody is on the right. They have a boat that can hold up to 2 beings. At no point on time may either of these be true: $$M_{...
-1
votes
3answers
303 views

Extremely hard prime factor based true-false statements [closed]

Let us suppose there are $n$ statements on the list. Each statement may be true or false. The first statement declares: I am true. Therefore, it could be true, or it could be false. After this, ...
11
votes
1answer
534 views

Bouncing Robots: Graphical Puzzle [closed]

Robots are indicated by the arrowhead shapes and the labels "r", "y", "b", "g". The label obviously corresponds to their color. The aim of the puzzle is to pick up the shapes and put them down in the ...
7
votes
3answers
808 views

Can you create a Minesweeper puzzle with 'information crossover'?

The object of this puzzle is to construct a Minesweeper grid with a special property. The grid can be any shape, but it must have four labeled squares around the outer edge. Like this: The four ...
27
votes
10answers
3k views

One prize, infinitely many choices

Having reached the final stage of a game show, you face an endless row of doors labelled $1$, $2$, $3$, ... The game show host has selected a whole dollar amount, and has put this exact amount as a ...
1
vote
2answers
530 views

If The Knights and Knaves got together [closed]

If the island of knights and knaves got together and there were n people, including a joker, how many questions would it take for all of the knights and knaves found the joker? Nobody knows who each ...
5
votes
2answers
637 views

What to do when the official Rubik's cube solving sequence breaks?

So, the official guide shows you exactly how to solve the white cross, first layer, etc. but on the second layer, assume you've completed every little square but one (and edge) and that there's 2 ...
11
votes
4answers
1k views

Optimization of area

You have a closed cord of length 100 meters which touches point $P$. There is a line $L$ whose closest point is 20 meters from point $P$. The value of a layout of cord is defined by the area ...
12
votes
2answers
4k views

Connect four towers by roads

Four guard towers are situated in a square formation of side length 1km. A general wants to build roads to connect the towers so that one can walk from any tower to any tower along the roads, possibly ...
15
votes
2answers
790 views

Santa Claus flies to the South Pole

It is a little known fact that Santa Claus is in fact a vampire. Why else would he spend so much time near the North Pole and travel only at night? Yes, he fears daylight! His problem is that ...
1
vote
2answers
389 views

Bottle rinsing with fixed amount of wash water

Given $L$ units of wash water, we want to wash out a vessel (eg, a milk bottle, honey jar, chemistry flask...) using a series of rinses that minimize the amount of Stuff other than water remaining in ...
5
votes
2answers
411 views

Land claim staking

It was traditional during the times of the Oregon Trail and the gold rush that men founding new towns were allowed to stake their claim on land upon arriving to the west coast. Suppose a man is ...